A statistical explanation of MaxEnt for ecologists

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A note on the large-angle anisotropies in the WMAP cut-sky maps

a r Xiv:076.575v1[astro-ph]5J un27IWARA˙NS˙2005˙Published International Journal of Modern Physics D c World Scientiﬁc Publishing Company A NOTE ON THE LARGE-ANGLE ANISOTROPIES IN THE WMAP CUT-SKY MAPS A.BERNUI Instituto Nacional de Pesquisas Espaciais –Divis˜a o de Astrof´ısica Av.dos Astronautas 175812227-010S˜a o Jos´e dos Campos –SP,Brazil B.MOTA,M.J.REBOUC ¸AS Centro Brasileiro de Pesquisas F´ısicas Rua Dr.Xavier Sigaud 15022290-180Rio de Janeiro –RJ,Brazil R.TAVAKOL Astronomy Unit –School of Mathematical Sciences Queen Mary,University of London Mile End Road,London E14NS,UK Received Day Month Year Recent analyses of the WMAP data seem to indicate the possible presence of large-angle anisotropy in the Universe.If conﬁrmed,these can have important consequences for our understanding of the Universe.A number of attempts have recently been made to establish the reality and nature of such anisotropies in the CMB data.Among these is a directional indicator recently proposed by the authors.A distinctive feature of this indicator is that it can be used to generate a sky map of the large-scale anisotropies of the CMB maps.Applying this indicator to full-sky temperature maps we found a statisticallysigniﬁcant preferred direction.The full-sky maps used in these analyses are known to have residual foreground contamination as well as complicated noise properties.Thus,here we performed the same analysis for a map where regions with high foreground contamination were removed.We ﬁnd that the main feature of the full-sky analysis,namely the presence of a signiﬁcant axis of asymmetry,is robust with respect to this masking procedure.Other subtler anomalies of the full-sky are on the other hand no longer present.Keywords :Observational cosmology;cosmic microwave background;large-scale anisotropies in CMB;large-angle anomalies in CMB.1.IntroductionThe wealth of high resolution data provided by the Wilkinson Microwave Anisotropy Probe (WMAP)1–2has conﬁrmed to very good approximation the standard cosmo-logical picture,which predicts a statistically isotropic Gaussian random cosmic mi-crowave background (CMB)temperature ﬂuctuations.Despite this success,several1IWARA˙NS˙2005˙Published2 A.Bernui,B.Mota,M.J.Rebou¸c as and R.Tavakollarge-scale anomalies in the CMB have been reported including indications of non-Gaussianity,3–4evidences for a North-South asymmetry,5and the so-called“low-ℓanomalies”such as the surprisingly small values of the CMB quadrupole and oc-topole moments,7and the alignment of the quadrupole and octupole moments,8–9(in this connection see Ref.10)whose direction has been suggested to extend to thehigher multipoles11(see also Ref.12for a detailed discussion).In addition,thereare also indications for a preferred axis of symmetry or directions of maximumasymmetry.13–18The possible origins of such unexpected anomalous features of CMB are at present the object of intense investigation,with several potential explanations,in-cluding unsubtracted foreground contamination and/or systematics,16unconsid-ered local eﬀects,19other mechanisms to break statistical isotropy,20and alsoextra-galactic origin(see Refs.5,8,11and13–15for details,and Ref.21for re-cent related references).If they turn out to have a cosmological nature,however,they could have far reaching consequences for our understanding of the Universe,in particular for the above-mentioned standard cosmological scenario.Recently we proposed22a new directional indicatorσ=σ(θ,φ),based on pair angular separation histogram(PASH),23to measure large-angle anisotropy in theWMAP data.An important feature of our indicator is that it can be used to gen-erate a sky map of large-angles anisotropies from CMB temperatureﬂuctuationsmaps.We have produced and studied in detailsσ−maps generated from the full-skyLILC,25‘cleaned’TOH,8and co-added2WMAP maps,and found a statisticallysigniﬁcant preferred direction in these WMAP maps,which agrees with the preferredasymmetry axes recently reported.5,15These results were found to be robust withrespect to the choice of the full-sky WMAP CMB maps employed.However,sincefull-sky maps are known to have residual foreground contamination25and compli-cated noise properties,2their choice in the“low-ℓ”studies is not a consensus.12,26Thus,the question arises as to whether our results hold for cut-sky maps.Our mainaim here,which extends and complements our previous work,22is to address thisquestion by considering the LILC map with a Kp2sky cut.To this end,in the nextsection we give an account of our large-angle anisotropy indicator,while in the lastsection we apply our indicator to the LILC map with a Kp2sky cut,and presentour main results and conclusions.rge-angle Anisotropy IndicatorFor a detailed discussion of the indicator brieﬂy presented in this section we referthe readers to Ref.22.The key point in the construction of our indicator is that a homogeneous distri-bution of points on a two-sphere S2is seen by an observer at the center of S2asisotropically distributed,and therefore deviations from homogeneity in this distri-bution give rise to anisotropies for this observer.Mutatis mutandis,since in CMB studies the celestial sphere is discretized into aIWARA˙NS˙2005˙Published Large-angle anisotropy in the WMAP data 3set of equal size pixels,with a temperature ﬂuctuation associated to each pixel,the idea in the CMB context is then to construct an indicator that measures deviation from homogeneity in the distribution of pixels with similar temperature.The ﬁrst step towards the construction of this indicator is subdivide a given CMB map into a number of submaps,each consisting of equal number of pixels with similar temperatures.The next step is to devise an indicator to measure the deviation from a homogeneous distribution of these pixels.The construction of our indicator,σ=σ(θ,φ)is based on angular separation histograms (PASH),which are obtained by counting the number of pairs of pixels whose angular separation αlies within small sub-intervals (bins)J i ∈(0,π],of length δα=π/N bins ,where J i = αi −δα2,i =1,2,...,N bins ,with the bin centers at αi =(i −1n (n −1)1N 1δαP (αi )=P (αi ),(3)where N =n (n −1)/2is the total number of pairs of pixels,P (αi )= α∈J i ηexp (α)/N is the probability that a pair of objects can be separated by an angular distance that lies in the interval J i ,P (αi )is the corresponding probability density,and where the coeﬃcient of the summation is a normalization factor.Equa-tion (3)makes it clear that the EPASH Φexp (α)gives the distribution of probability of ﬁnding pairs of points on the sky sphere with any angular separation αi ∈(0,π].a We denote the diﬀerence between the mean PASH (MPASH), Φobs (αi ) ,calcu-lated from the observational data,and the EPASH Φexp (αi ),obtained from an statistically isotropic distribution of pixels,asΥ(αi )≡ Φobs (αi ) −Φexp (αi ).(4)2sin α.This is the limit of a statistically isotropic distribution of points in S 2as the number of points go to inﬁnity.One can thus quantify anisotropy by calculating the departure of the mean observed probability distribution Φobs (αi ) from it,namely Φobs (αi ) −Φexp (αi ).IWARA˙NS˙2005˙Published4 A.Bernui,B.Mota,M.J.Rebou¸c as and R.TavakolIn practice,the expectedΦexp(αi)for a statistically isotropic map is obtained sim-ply by scrambling a CMB map multiple times,and averaging over the resultinghistograms.Lastly,to quantify anisotropy,we distill the histogramΥ(αi)into a single num-ber,by deﬁning the indicatorσ=σ(θ,φ)as the variance ofΥ(αi)(which has zeromean),namely1σ2(θ,φ)≡2ℓ+1 m|bℓm|2.(6) It then follows that if a large-angle asymmetry is present in the CMB temperaturedistribution,it should signiﬁcantly aﬀect theσ−map on the corresponding angularscales(low-ℓmultipoles).In the next section,we shall generate theσ−maps from LILC map with a Kp2 sky cut,study its main features,and make a comparison with our previous resultsfor the full-sky CMB maps.223.Main Results and ConclusionsGiven that the large-scale angular correlations are nonlocal,σ(θ,φ),calculated overa30◦-radius cap centered at(θ,φ),can be though of as a measure of the anisotropyin the direction(θ,φ).In our previous work22the strategy was to obtainσfor a setof12,288caps of radius30◦co-centered with the same number of pixels generatedby HEALPix with N side=32,evenly covering the entire celestial sphere.Theresulting directional map of anisotropy was the so-calledσ−map.We applied thisnew anisotropy indicator to three CMB WMAP maps:the LILC25and the TOH8maps(which are two diﬀerently foreground cleaned full-sky maps resulting from thecombination of theﬁve frequency bands:K,Ka,Q,V,and W CMB maps measuredIWARA˙NS˙2005˙PublishedLarge-angle anisotropy in the WMAP data5 by the WMAP satellite),and the co-added map,which is a weighted combinationof the Q,V,and W WMAP maps.The resultingσ−map were found to be anisotropic.Brieﬂy,there is a prominent spot with very highσon the southeastern corner,with a well deﬁned maximumat(b≃115◦,l≃235◦),which is close(by16◦)to the direction recently indicatedin Ref.11.It was further shown(by a standard spherical harmonics expansion)that the LILCσ−map deviates from isotropy in a statistically signiﬁcant way,withanomalously high(>95%CL)dipole,quadrupole and octupole components(seeFigs.3and4of Ref.22).The higher components on the other hand fall withinthe expected values.This clearly indicates that the LILC map is not statisticallyisotropic.Finally,we noted that the quadrupole component has a very peculiarshape,being very symmetric around an axis slightly oﬀthe galactic North-South.Indeed,82%of the total power in D2comes from an axisymmetric component inthe direction(b=10◦,l=289◦),somewhat close to the axes of symmetry of thetemperature quadrupole and octupole found in Ref.8(about24◦from both).As previously mentioned,however,there is no consensus as to whether the full sky cleaned maps available are indeed free of signiﬁcant galactic contamination.Thequestion then arises as to whether one should study the full sky maps or conﬁnethe analysis to regions where such contamination is small.In view of the lack of consensus on how to perform the data analysis,here we examine the robustness of our previous results by investigating the LILC map afterthe application of the Kp2mask(hereafter the LILC-Kp2map),which discards thetemperatureﬂuctuations of15.3%of the total number of pixels,mainly concentratedaround the galactic plane.Note that some of the caps with centers close to but outside the Kp2mask would still overlap with the mask itself.If the intersection region is too large theσvaluewould be largely an artifact os the masking procedure.On the other hand,if wewere to exclude all caps were any overlapping occurs,we would lose information onover half of the sky.To achieve a balance,we shall disregard caps that obey eitherof the following criteria:•have the cap center within the Kp2mask,and•have over15%of pixels within the Kp2mask.With this critical value of15%for the maximum number of overlapping pixelstypically the value ofσcalculated for the same cap in both the LILC and LILC-Kp2maps diﬀer by less than10%.As can be seen in Fig.1,there is a spot of very highσin the southeastern corner of the map,which coincides in both direction and magnitude with the one found inthe full LILCσ−map.22The fact that this spot lies well outside the region of signif-icant galactic contamination suggests it is not the result of galactic contamination.The possibility remains,however,that it is caused by some unaccounted foregroundcontamination.Such contamination however would unlikely to aﬀect the diﬀerentIWARA˙NS˙2005˙Published6 A.Bernui,B.Mota,M.J.Rebou¸c as and R.Tavakolfrequency bands in exactly the same way.To verify whether this is the case,wecalculated theσ−map for the Q,V and W bands separately,along with the co-added map27,which is considered the most reliable map for CMB studies25,26(seeFig.2).The resulting maps are almost identical,ground contamination may not account for the previouslyanisotropy.Fig.1.Theσ−map for the LILC-Kp2map.This result was obtainedcaps with apertureθ0=30◦,following the criteria outlined above.Q VW CoaddedFig.2.Theσ−map for the WMAP’s Q-,V-and W-bands,along with the combined co-addedmap,using the Kp2mask.In all maps the highσvalue is apparent.Several new smaller highσspots are also in evidence near the mask region,but they are probably just artifacts of the masking procedure.As discussed in22themain features of the resultingσ−map are robust with respect to the number ofspherical caps used to cover the celestial sphere or the cap apertureθ0.IWARA˙NS˙2005˙PublishedLarge-angle anisotropy in the WMAP data7 To obtain more quantitative information about the observed anisotropy,we fol-lowed the procedure of our previous work and calculated the power spectrum of theLILC-Kp2σ−map using the Anafast subroutine in Healpix28.Since we are nowdealing with an incomplete sphere,the spherical harmonics are no longer orthogo-nal,and the values obtained must be handled with care.The D l values are depictedin Fig.3,along with the corresponding full sky values for comparison.It is clearthat the dipole component of theσ−map is even larger for the LILC-Kp2than forthe full sky LILC.This is consistent with the presence of an axis of asymmetry,again conﬁrming our earlier results.The direction of theσ−map dipole changes,however,from(b=141◦,l=240◦)in the full sky map to(b=150◦,l=209◦),inthe LILC-Kp2map,a diﬀerence of19◦.The quadrupole and octupole componentson the other hand are comparatively smaller in the LILC-Kp2map,probably dueto the fact that many of the highσstructures other than the large spot in thesoutheastern quadrant are now excluded by the Kp2mask.IWARA˙NS˙2005˙Published8 A.Bernui,B.Mota,M.J.Rebou¸c as and R.Tavakolliterature obtained using diﬀerent methods.This strongly suggests that either theobservable universe is intrinsically anisotropic,or that there are other,subtler formsof foreground contamination that have not yet been taken into account.Among theproposed explanations for the global preferred direction,it has been suggested thatit could be due to a non-trivial topology of the spatial section of the universe12,7(formore details on cosmic topology see the review articles Refs.29,and,e.g.,Refs.30,31).If topology is indeed the origin,the indicatorΥis promising in distinguishingbetween diﬀerent topologies,as has been demonstrated by computer simulations inRef.23.These are very exciting possibilities,and are worthy of further investigation.AcknowledgmentsWe thank CNPq,PCI-CBPF/CNPq,PCI-INPE/CNPq-MCT and PPARC for thegrants under which this work was carried out.We acknowledge use of the LegacyArchive for Microwave Background Data Analysis(LAMBDA).Some of the resultsin this paper have been derived using the HEALPix package.References1. 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统计结果的英语作文

统计结果的英语作文Title: Analyzing Statistical Data: Insights and Implications.Statistical data, often considered the backbone of informed decision-making, plays a pivotal role in various fields, from business analytics to scientific research. In today's world, where information is at our fingertips, understanding and interpreting statistical data has become increasingly important. This article delves into the essence of statistical analysis, exploring its applications, methods, and the insights it reveals.Applications of Statistical Data.Statistical data finds its application in almost every domain of human activity. In business, it helps companies track performance, predict market trends, and make informed decisions about investment, production, and sales. In medicine, statistical analysis is used to evaluate theeffectiveness of treatments, understand disease patterns, and predict health outcomes. In social sciences, it aids in understanding population behaviors, trends, and patterns.Methods of Statistical Analysis.Statistical analysis involves a range of techniques and methods to process and interpret data. Descriptive statistics, for instance, summarize data through measures like mean, median, mode, and standard deviation, providing a snapshot of the data's central tendency and dispersion. Inferential statistics, on the other hand, allows researchers to draw conclusions about a population based on a sample. Techniques such as regression analysis, ANOVA, and chi-square tests are commonly used to test hypotheses and identify relationships between variables.Insights from Statistical Data.Statistical data, when analyzed correctly, can yield profound insights. For instance, in business, it can reveal patterns in customer behavior, market trends, and productperformance. This information can be used to refine marketing strategies, improve product quality, and increase customer satisfaction. In the medical field, statistical analysis can help identify risk factors for diseases, predict patient outcomes, and evaluate the effectiveness of new treatments.Challenges and Limitations.While statistical data can provide valuable insights,it also has its limitations. One of the main challenges is ensuring data quality. Inaccuracies, biases, and incomplete data can lead to misleading conclusions. Additionally, statistical analysis often assumes a certain level of randomness and normality in data, which may not always be the case. Furthermore, statistical significance does not always translate to practical significance, meaning a finding may be statistically significant but may not have a meaningful impact in real-world scenarios.Conclusion.Statistical data, when interpreted correctly, can provide valuable insights across various fields. It helps us understand patterns, trends, and relationships in data, enabling us to make informed decisions and predictions. However, it is important to remember that statistical analysis has its limitations, and it should always be used in conjunction with other forms of evidence and expertise. By harnessing the power of statistical data, we can gain a deeper understanding of the world and make more informed and effective decisions.。

maxent原版英文说明

maxent原版英文说明RESM 575 Spatial AnalysisSpring 2010Lab 6 Maximum EntropyAssigned: Monday March 1Due: Monday March 820 pointsThis lab exercise was primarily written by Steven Phillips, Miro Dudik and Rob Schapire, with support from AT&T Labs-Research, Princeton University, and the Center for Biodiversity and Conservation, American Museum of Natural History. This lab exercise is based on their paper and data:Steven J. Phillips, Robert P. Anderson , Robert E. Schapire.Maximum entropy modeling of species geographic distributions.Ecological Modelling, Vol 190/3-4 pp 231-259, 2006.My goal is to give you a basic introduction to use of the MaxEnt program for maximum entropy model ing of species’ geographic distributions.The environmental data consist of climatic and elevational data for South America, together with a potential vegetation layer. The sample species the authors used will be Bradypus variegatus, the brown-throated three-toed sloth.NOTE on the Maxent softwareThe software consists of a jar file, maxent.jar, which can be used on any computer running Java version 1.4 or later. It can be downloaded, along with associated literature, from /~schapire/maxent. If you are using Microsoft Windows (as we assume here), you should also download the file maxent.bat, and save it in the same directory as maxent.jar. The website has a file called “readme.txt”, which contains instructions for installing the program on your computer.The software has already been downloaded and installed on the machines in 317 Percival.First go to the class website and download the maxent-tutorial-data.zip file.Extract it to the c:/temp folder which will create a c:/temp/tutorial-datadirectory.Find the maxent directory on the c:/ drive of your computer and simply click on the file maxent.bat. The following screen will appear:2To perform a run, you need to supply a file containing presence localities (“samples”), a directory containing environmental variables, and an output directory. In our case, the presence localities are in the file“c:\temp\tutorial-data\samples\bradypus.csv”, the environmental layers are in the directory “layers”, and the outputs are going to go in the directory “outputs”. You can enter these locations by hand, or browse for them. While browsing for the environmental variables, remember that you are looking for the directory that contains them –you don’t need to browse down to the files in the directory. After entering or browsing for the files for Bradypus, the program looks like this:3The file “samples\bradypus.csv” contains the presence localities in .csv format. The first few lines are as follows:species,longitude,latitudebradypus_variegatus,-65.4,-10.3833bradypus_variegatus,-65.3833,-10.3833bradypus_variegatus,-65.1333,-16.8bradypus_variegatus,-63.6667,-17.45bradypus_variegatus,-63.85,-17.4There can be multiple species in the same samples file, in which case more species would appear in the panel, along with Bradypus. Other coordinate systems can be used, other than latitude and longitude, as long as the samples file and environmental layers use the same coordinate system. The “x” coordinate should come before the “y” coordinate in the samples file.The directory “layers” contains a number of ascii ras ter grids (in ESRI’s .asc format), each of which describes an environmental variable. The grids must all have the same geographic bounds and cell size. MAKE SURE YOUR ASCII FILES HAVE THE .asc EXTENSION!!!!!!!!! One of our variables, “ecoreg”, is a cate gorical variable describing potential vegetation classes. You must tell the program which variables are categorical, as has been done in the picture above.Doing a runSimply press the “Run” button. A progress monitor describes the steps being taken. After the environmental layers are loaded and some initialization is done, progress towards training of the maxent model is shown like this:The “gain” starts at 0 and increases towards an asymptote during the run. Maxent is a maximum-likelihood method, and what it is generating is a probability distribution over pixels in the grid. Note that it isn’t calculating “probability of occurrence” – its probabilities are typically very small values, as they must sum to 1 over the whole grid. The gain is a measure of the likelihood of the samples; for example, if the gain is 2, it means that the average sample likelihood is exp(2) ≈ 7.4 times higher than that of a random background pixel. The uniform distribution has gain 0, so you can interpret the gain as representing how much better the distribution4fits the sample points than the uniform distribution does. The gain is closely related to “deviance”, as used in statistics.The run produces a number of output files, of which the most important is an html f ile called “bradypus.html”. Part of this file gives pointers to the other outputs, like this:Looking at a predictionTo see what other (more interesting) content there can be inc:\temp\tutorial-data\outpus\bradpus_variegatus.html, we will turn on a couple of options and rerun the model. Press the “Make pictures of predictions” button, then c lick on “Settings”, and type “25” in the “Random test percentage” entry. Lastly, press the “Run” button again. You may have to say “Replace All” for this new run. After the run completes, the file bradypus.html contains this picture:5The image uses colors to show prediction strength, with red indicating strong prediction of suitable conditions for the species, yellow indicating weak prediction of suitable conditions, and blue indicating very unsuitable conditions. For Bradypus, we see strong prediction through most of lowland Central America, wet lowland areas of northwestern South America, the Amazon basin, Caribean islands, and much of the Atlantic forests in south-eastern Brazil. The file pointed to is an image file (.png) that you can just click on (in Windows) or open in most image processing software.The test points are a random sample taken from the species presence localities. Test data can alt ernatively be provided in a separate file, by typing the name of a “Test sample file” in the Settings panel. The test sample file can have test localities for multiple species.Statistical analysisThe “25” we entered for “random test percentage” told the program to randomly set aside 25% of the sample records for testing. This allows the program to do some simple statistical analysis. It plots (testing and training) omission against threshold, and predicted area against threshold, as well as the receiver operating curve show below. The area under the ROC curve (AUC) is shown here, and if test data are available, the standard error of the AUC on the test data is given later on in the web page.A second kind of statistical analysis that is automatically done if test data are available is a test of the statistical significance of the prediction, using a binomial test of omission. For Bradypus, this gives:6Which variables matter?To get a sense of which variables are most important in the model, we can run a jackknife test, by selecting the “Do jackknife to measure variable important” checkbox . When we press the “Run” button again, a number of models get created. Each variable is excluded in turn, and a model created with the remaining variables. Then a model is created using each variable in isolation. In addition, a model is created using all variables, as before. The results of the jackknife appear in the “bradypus.html” files in three bar charts, and the first of these is shown below.7We see that if Maxent uses only pre6190_l1 (average January rainfall) it achieves almost no gain, so that variable is not (by itself) a good predictor of the distribution of Bradypus. On the other hand, October rainfall (pre6190_l10) is a much better predictor. Turning to the lighter blue bars, it appears that no variable has a lot of useful information that is not already contained in the others, as omitting each one in turn did not decrease the training gain much.The bradypus_variegatus.html file has two more jackknife plots, using test gain and AUC in place of training gain. This allows the importance of each variable to be measure both in terms of the model fit on training data, and its predictive ability on test data.How does the prediction depend on the variables?Now press the “Create response curves”, deselect the jackknife option, and rerun the model. This results in the following section being added to the“bradypus_variegatus.html” file:8Each of the thumbnail images can be clicked on to get a more detailed plot. Looking at frs6190_ann, we see that the response is highest for frs6190_ann = 0, and is fairly high for values of frs6190_ann below about 75. Beyond that point, the response drops off sharply, reaching -50 at the top of th e variable’s range.So what do the values on the y-axis mean? The maxent model is an exponential model, which means that the probability assigned to a pixel is proportional to the exponential of some additive combination of the variables. The response curve above shows the contribution of frs6190_ann to the exponent. A difference of 50 in the exponent is huge, so the plot for frs6190_ann shows a very strong drop in predicted suitability for large values of the variable.On a technical note, if we are modeling interactions between variables (by using product features) as we are for Bradypus here, then the response curve for one variable will depend on the settings of other variables. In this case, the response curves generated by the program have all other variables set to their mean on the set of presence localities.Note also that if the environmental variables are correlated, as they are here, the response curves can be misleading. If two closely correlated variables have strong response curves that are near opposites of each other, then for most pixels, the combined effect of the two variables may be small. To see how the response curve depends on the other variables in use, try comparing the above picture with the response curve obtained when using only frs6190_ann in the model (by deselecting all other variables).Feature types and response curvesResponse curves allow us to see the difference between different feature types. Deselect the “auto features”, select “Threshold features”, and press the “Run” button again. Take a look at the resulting feature profiles –you’ll notice that they are all step functions, like this one for pre6190_l10:9If the same run is done using only hinge features, the resulting feature profile looks like this:The outline of the two profiles is similar, but they differ because the different classes of feature types are limited in the shapes of response curves they are capable of modeling. Using all classes together (the default, given enough samples) allows many complex response curves to be accurately modeled.10SWD FormatThere is a second input format that can be very useful, especially when your environmental grids are very large. For lack of a better name, it’s called “samples with data”, or just SWD.The SWD version of our Bradypus file, called “bradypus_swd.csv”, starts like this:species,longitude,latitude,cld6190_ann,dtr6190_ann,ecoreg,frs6190_ann,h_dem,pre6190_ann,pre6190_l10,pre61 90_l1,pre6190_l4,pre6190_l7,tmn6190_ann,tmp6190_ann,tmx6190_ann,vap6190_annbradypus_variegatus,-65.4,-10.3833,76.0,104.0,10.0,2.0,121.0,46.0,41.0,84.0,54.0,3.0,192.0,266.0,337.0,279.0 bradypus_variegatus,-65.3833,-10.3833,76.0,104.0,10.0,2.0,121.0,46.0,40.0,84.0,54.0,3.0,192.0,266.0,337.0,279.0 bradypus_variegatus,-65.1333,-16.8,57.0,114.0,10.0,1.0,211.0,65.0,56.0,129.0,58.0,34.0,140.0,244.0,321.0,221.0 bradypus_variegatus,-63.6667,-17.45,57.0,112.0,10.0,3.0,363.0,36.0,33.0,71.0,27.0,13.0,135.0,229.0,307.0,202.0 bradypus_variegatus,-63.85,-17.4,57.0,113.0,10.0,3.0,303.0,39.0,35.0,77.0,29.0,15.0,134.0,229.0,306.0,202.0It can be used in place of an ordinary samples file. The difference is only that the program doesn’t need to look in the environmental layers to get values for the variables at the sample points. The environmental layers are thus only used to get “background” pixels – pixels where the species hasn’t necessarily been found. In fact, the background pixels can also be specified in a SWD format file, in which case the “species” column is ignored. The file “b ackground.csv” has 10,000 background data points in it. The first few look like this:background,-61.775,6.175,60.0,100.0,10.0,0.0,747.0,55.0,24.0,57.0,45.0,81.0,182.0,239.0,300.0,232.0 background,-66.075,5.325,67.0,116.0,10.0,3.0,1038.0,75.0,16.0,68.0,64.0,145.0,181.0,246.0,331.0,234.0 background,-59.875,-26.325,47.0,129.0,9.0,1.0,73.0,31.0,43.0,32.0,43.0,10.0,97.0,218.0,339.0,189.0 background,-68.375,-15.375,58.0,112.0,10.0,44.0,2039.0,33.0,67.0,31.0,30.0,6.0,101.0,181.0,251.0,133.0 background,-68.525,4.775,72.0,95.0,10.0,0.0,65.0,72.0,16.0,65.0,69.0,133.0,218.0,271.0,346.0,289.0We can run Maxent with “bradypus_swd.csv” as the samples file and “background.csv” (both located in the “swd” directory) as the environmental layers file. Try running it – yo u’ll notice that it runs much faster, because it doesn’t have to load the big environmental grids. The downside is that it can’t make pictures or output grids, because it doesn’t have all the environmental data. The way to get around this is to use a “projection”, described below.Batch runningSometimes you need to generate a number of models, perhaps with slight variations in the modeling parameters or the inputs. This can be automated using command-line arguments, avoiding the repetition of having to click and type at the program interface. The command line arguments can either be given from a command window (a.k.a. shell), or they can defined in a batch file. Take a look at the file “batchExample.bat” (for example, using Notepad). It contains th e following line:java -mx512m -jar maxent.jar environmentallayers=layers togglelayertype=ecoreg samplesfile=samples\bradypus.csv outputdirectory=outputs redoifexists autorunThe effect is to tell the program where to find environmental layers and samples file and where to put outputs, to indicate that the ecoreg variable is categorical. The “autorun” flag tells the program to start running immediately, without waiting for the “Run” button to be pushed. Now try clicking on the file, to see what it does.Many aspects of the Maxent program can be controlled by command-line arguments –press the “Help” button to see all the possibilities.Multiple runs can appear in the same file, and they will simply be run one after the other. You can change the default values of most parameters by adding command-line arguments to the “maxent.bat” file.Regularization.The “regularization multiplier” parameter on the “settings” panel affects how focused the output distribution is – a smaller value will result in a more localized output distribution that fits the given presence records better, but is more prone to overfitting. A larger value will give a more spread-out prediction. Try changing the multiplier, and look at the pictures produced. As an example, setting the multiplier to 3 makes the following picture, showing a much more diffuse distribution than before:ProjectingA model trained on one set of environmental layers can be “projected” by applying it to another set of environmental layers. Situations where projections are needed include modeling species distributions under changing climate conditions, and modeling invasive species. Here we’re going to use projection for a very simple task: making an output grid and associated picture when the samples and background are in SWD format. Type or browse in the samples file entry to point to the file“swd\bradypus_swd.csv”, and similarly for the environmental layers in“swd\background.csv”, then enter the “layers” directory in the “Projection Layers Dir ectory”, as pictured below.When you press “Run”, a model is trained on the SWD data, and then projected onto the full grids in the “layers” directory. The output grid is called“bradypus_variegatus_layers.asc”, and in general, the projection direct ory name is appended to the species name, in order to distinguish it from the standard(un-projected) output. If “make pictures of predictions” is selected, a picture of the projected model will appear in the “bradypus_variegatus.html” file.NOTE: ascii files can be converted into ESRI Grids by using the Ascii to Raster grid command in ArcToolbox.Your assignment is to convert the ascii file into a grid format, display it in ArcMap and create a map layout. Provide an appropriate legend showing the probabilities. Print it out and turn in to class next week.。

Constants and Variations From Alpha to Omega

a rXiv:g r-qc/298v 123Sep22Constants and Variations:From Alpha to OmegaJohn D.Barrow DAMTP Centre for Mathematical Sciences Cambridge University Cambridge CB30WA UK February 7,2008Abstract We review some of the history and properties of theories for the vari-ation of the gravitation and ﬁne structure ’constants’.We highlight some general features of the cosmological models that exist in these theories with reference to recent quasar data that is consistent with time-variation in alpha since a redshift of 3.5.The behaviour of a simple class of varying-alpha cosmologies is outlined in the light of all the observational con-straints.We discuss the key role played by non-zero vacuum energy and curvature in turning oﬀthe variation of constants in these theories and the issue of comparing extra-galactic and local observational data.We also show why black hole thermodynamics does not enable us to distinguish between time variations of diﬀerent constants.1IntroductionThere are a number of reasons why the possibility of varying constants should be taken seriously [1].First,we know that the best candidates for uniﬁcation of the forces of nature in a quantum gravitational environment only seem to exist in ﬁnite form if there are many more dimensions of space than the three that we are familiar with.This means that the true constants of nature are deﬁned in higher dimensions and the three-dimensional shadows we observe are not fundamental and do not need to be constant.Any slow change in the scale of the extra dimensions would be revealed by measurable changes in our three-dimensional ’constants’.Second,we appreciate that some apparent constant might be determined partially or completely by some spontaneous symmetry-breaking processes in the very early universe.This introduces an irreducible1random element into the values of those constants.They may be diﬀerent in diﬀerent parts of the universe.The most dramatic manifestation of this process is provided by the chaotic and eternal inﬂationary universe scenarios.Third, any outcome of a theory of quantum gravity will be intrinsically probabilistic. It is often imagined that the probability distributions for observables will be very sharply peaked but this may not be the case for all possibilities.Thus,the value of G or˙G might be predicted to be spatially varying random variables. Fourth,the non-uniqueness of the vacuum state for the universe would allow other deals of the constants to have occurred in diﬀerent places.At present we have no idea why any of the constants of Nature take the numerical values they do.Fifth,the observational limits on possible variations are often very weak (although they can be made to sound strong by judicious parametrisations).For example,the cosmological limits on varying G tell us only that˙G/G≤10−2H0, where H0is the present Hubble rate.However,the last reason to consider varying constants is currently the most compelling.For theﬁrst time there is a body of detailed astronomical evidence for the time variation of a traditional constant.The observational programme of Webb et al[2,3]has completed detailed analyses of three separate quasar absorption line data sets taken at Keck andﬁnds persistent evidence consistent with theﬁne structure constant,α,having been smaller in the past,at z=1−3.5.The shift in the value ofαfor all the data sets is given provisionally by∆α/α=(−0.66±0.11)×10−5. This result is currently the subject of detailed analysis and reanalysis by the observers in order to search for possible systematic biases in the astrophysical environment or in the laboratory determinations of the spectral lines.Theﬁrst investigations of time-varying constants were those made by Lord Kelvin and others interested in possible time-variation of the speed of light at the end of the nineteenth century.In1935Milne devised a theory of gravity, of a form that we would now term’bimetric’,in which there were two times –one(t)for atomic phenomena,one(τ)for gravitational phenomena–linked byτ=log(t/t0).Milne[4]required that the’mass of the universe’(what we would now call the mass inside the particle horizon M≈c3G−1t)be constant. This required G∝t.Interestingly,in1937the biologist J.B.S.Haldane took a strong interest in this theory and wrote several papers[5]exploring its conse-quences for the evolution of life.The argued that biochemical activation energies might appear constant on the t timescale yet increase on theτtimescale,giving rise to a non-uniformity in the evolutionary process.Also at this time there was widespread familiarity with the mysterious’large numbers’O(1040)and O(1080)through the work of Eddington(although they hadﬁrst been noticed by Weyl[6]–see ref.[7]and[1]for the history).These two ingredients were merged by Dirac in1937in a famous development(supposedly written on his honeymoon)that proposed that these large numbers(1040)were actually equal, up to small dimensionless factors.Thus,if we form N∼c3t/Gm n∼1080, the number of nucleons in the visible universe,and equate it to the square of N1∼e2/Gm2n∼1040,the ratio of the electrostatic and gravitational forces between two protons then we are led to conclude that one of the constants, e,G,c,h,m n must vary with time.Dirac[8]chose G∝t−1to carry the time2variation.Unfortunately,this hypothesis did not survive very long.EdwardTeller[9]pointed out that such a steep increase in G to the past led to huge in-creases in the Earth’s surface temperature in the past.The luminosity of the sunvaries as L∝G7and the radius of the Earth’s orbit as R∝G−1so the Earth’ssurface temperature T⊕varies as(L/R2)1/4∝G9/4∝t−9/4and would exceed the boiling point of water in the pre-Cambrian era.Life would be eliminated.Gamow subsequently suggested that the time variation needed to reconcile the large number coincidences be carried by e rather than G,but again this strong variation was soon shown to be in conﬂict with geophysical and radioactive de-cay data.This chapter was brought to an end by Dicke[10]who pointed out that the N∼N21large number coincidence was just the statement that t,the present age of the universe when our observations are being made,is of order the main sequence stellar lifetime,t ms∼(Gm2n/hc)−1h/m n c2∼1010yrs,and therefore inevitable for observers made from elements heavier than hydrogen and helium.Dirac never accepted this anthropic explanation for the large num-ber coincidences but curiously can be found making exactly the same type of anthropic argument to defend his own varying G theory by highly improbable arguments(that the Sun accretes material periodically during its orbit of the galaxy and this extra material cancels out the eﬀects of overheating in the past) in correspondence with Gamow in1967(see[1]for fuller details).Dirac’s proposal acted as a stimulus to theorists,like Jordan,Brans and Dicke[11],to develop rigorous theories which included the time variation of G self-consistently by modelling it as arising from the space-time variation of some scalarﬁeldφ(x,t)whose motion both conserved energy and momentum and created its own gravitationalﬁeld variations.In this respect the geometric structure of Einstein’s equations provides a highly constrained environment to introduce variations of’constants’.Whereas in Newtonian gravity we are at liberty to introduce a time-varying G(t)into the law of gravity byG(t)MmF=−T ab(2)c4then taking a covariant divergence and using∇a G ab=0,together with energy-momentum conservation(∇a T ab=0)requires that∇G≡0and no variationsare possible in eq.(2).Brans-Dicke theory is a familiar example of how the addition of an extra piece to T ab together with the dynamics of a G(φ)ﬁelds makes a varying G theory possible.Despite the simplicity of this lesson in the context of a varying G theory the lesson was not taken on board when considering the variations of other non-gravitational constants and the literature3is full of limits on their possible variation which have been derived by considering a theory in which the time-variation is just written into the equations which hold when the constant does not vary.Recently,the interest in the possibility thatαvaries in time has led to theﬁrst extensive exploration of simple self-consistent theories in which a variations occur through the variation of some scalarﬁeld. 2Brans-Dicke Theories2.1Equations and solutionsConsider the paradigmatic case of Brans-Dicke(BD)theory[11]toﬁx theoret-ical ideas about varying G.The form of the general solutions to the Friedmann metric in BD theories are fully understood[13],[14].There are three essential ﬁeld equations for the evolution of BD scalarﬁeldφ(t)and the expansion scale factor a(t)in a BD universe3˙a2φ−3˙a˙φ2˙φ2a2(3)¨φ+3˙a3+2ωBD(ρ−3p)(4)˙ρ+3˙a1+2ωBD/3φ(t)=φ0t[2(1−3Γ)/[4+3ω(1−Γ2)](10) At late times they approach particular exact power-law solutions for a(t)and φ(t)and the evolution is’Machian’in the sense that the cosmological evolution is driven by the matter content rather than by the kinetic energy of the freeφﬁeld.In the radiation era this particular solution is the standard general relativity solution:a(t)=t1/2;φ−1∝G=constant(11) For p=0the solutions have the forma(t)=t(2−n)/3;φ−1∝G∝t−n,(12) which continues until the curvature term takes over the expansion.Here,n is related to the constant Brans-DickeωBD parameter by2n≡An interesting particular example of this problem is given by the power-law solutions above for the case withΓ=−1.This is equivalent to the universe being dominated by a vacuum energy and leads to power-law accelerated expansion in BD theory witha(t)=t1more general theories in which all the uniﬁed interactions vary[25,26,27].Theconstraint imposed on varyingαby the need to bring about uniﬁcation at high energy is likely to be signiﬁcant but the complexities of analysing the simulta-neous variation of all the constants involved in the supersymmetric version ofthe standard model are considerable.At the most basic level we recognise that any time variation in theﬁne structure could be carried by either or both of theelectromagnetic or weak couplings above the electroweak scale.The idea that the charge on the electron,or theﬁne structure constant,mightvary in cosmological time was proposed in1948by Teller,[9],who suggested thatα∝(ln t)−1was implied by Dirac’s proposal that G∝t−1and the numerical coincidence thatα−1∼ln(hc/Gm2pr),where m pr is the proton ter,in 1967,Gamow[28]suggestedα∝t as an alternative to Dirac’s time-variationof the gravitation constant,G,as a solution of the large numbers coincidences problem and in1963Stanyukovich had also considered varyingα,[29],in this context.However,this power-law variation in the recent geological past was soon ruled out by other evidence[30].There are a number of possible theories allowing for the variation of theﬁne structure constant,α.In the simplest cases one takes c and to be con-stants and attributes variations inαto changes in e or the permittivity of free space(see[31]for a discussion of the meaning of this choice).This is done by letting e take on the value of a real scalarﬁeld which varies in space and time(for more complicated cases,resorting to complexﬁelds undergoing spon-taneous symmetry breaking,see the case of fast tracks discussed in[32]).Thus e0→e=e0ǫ(xµ),whereǫis a dimensionless scalarﬁeld and e0is a constant denoting the present value of e.This operation implies that some well estab-lished assumptions,like charge conservation,must give way[33].Nevertheless, the principles of local gauge invariance and causality are maintained,as is the scale invariance of theǫﬁeld(under a suitable choice of dynamics).In addition there is no conﬂict with local Lorentz invariance or covariance.With this set up in mind,the dynamics of our theory is then constructed asfollows.Since e is the electromagnetic coupling,theǫﬁeld couples to the gauge ﬁeld asǫAµin the Lagrangian and the gauge transformation which leaves the action invariant isǫAµ→ǫAµ+χ,µ,rather than the usual Aµ→Aµ+χ,µ.The gauge-invariant electromagneticﬁeld tensor is thereforeFµν=1−gFµνFµν.(19) and the dynamics of theǫﬁeld are controlled by the kinetic termSǫ=−1l2 d4x√ǫ2,(20) 7as in dilaton theories.Here,l is the characteristic length scale of the theory, introduced for dimensional reasons.This constant length scale gives the scale down to which the electricﬁeld around a point charge is accurately Coulombic. The corresponding energy scale, c/l,has to lie between a few tens of MeV and Planck scale,∼1019GeV to avoid conﬂict with experiment.Our generalisation of the scalar theory proposed by Bekenstein[19]described in ref.[22,21,20,24]includes the gravitational eﬀects ofψand gives theﬁeld equations:Gµν=8πG T matterµν+Tψµν+T emµνe−2ψ .(21) The stress tensor of theψﬁeld is derived from the lagrangian Lψ=−ωe−2ψL em(22)ωwhere we have deﬁned the coupling constantω=(c)/l2.This constant is of order∼1if,as in[?],the energy scale is similar to Planck scale.It is clear that L em vanishes for a sea of pure radiation since then L em=(E2−B2)/2= 0.We therefore expect the variation inαto be driven by electrostatic and magnetostatic energy-components rather than electromagnetic radiation.In order to make quantitative predictions we need to know how much of the non-relativistic matter contributes to the RHS of Eqn.(22).This is parametrised byζ≡L em/ρ,whereρis the energy density,and for baryonic matter L em= E2/2.For protons and neutronsζp andζn can be estimated from the electro-magnetic corrections to the nucleon mass,0.63MeV and−0.13MeV,respec-tively[42].This correction contains the E2/2contribution(always positive), but also terms of the form jµaµ(where jµis the quarks’current)and so cannot be used directly.Hence we take a guiding valueζp≈ζn∼10−4.Furthermore the cosmological value ofζ(denotedζm)has to be weighted by the fraction of matter that is non-baryonic,a point ignored in the literature[19].Hence,ζm depends strongly on the nature of the dark matter and can take both positive and negative values depending on which of Coulomb-energy or magnetostatic energy dominates the dark matter of the Universe.It could be thatζCDM≈−1 (superconducting cosmic strings,for which L em≈−B2/2),orζCDM≪1(neu-trinos).BBN predicts an approximate value for the baryon density ofΩB≈0.03 with a Hubble parameter of h0≈0.6,implyingΩCDM≈0.3.Thus depending on the nature of the dark matterζm can be virtually anything between−1and +1.The uncertainties in the underlying quark physics and especially the con-stituents of the dark matter make it diﬃcult to impose more certain bounds on ζm.We should not confuse this theory with other similar variations.Bekenstein’s theory does not take into account the stress energy tensor of the dielectricﬁeld in Einstein’s equations,and their application to cosmology.Dilaton theories predict a global coupling between the scalar and all other matterﬁelds.As a result they predict variations in other constants of nature,and also a diﬀerent dynamics to all the matter coupled to electromagnetism.An interesting appli-8cation of our approach has also recently been made to braneworld cosmology in [34].3.1The cosmological equationsAssuming a homogeneous and isotropic Friedmann metric with expansion scale factor a(t)and curvature parameter k in eqn.(21),we obtain theﬁeld equations (c≡1)˙a3 ρm(1+ζm exp[−2ψ])+ρr exp[−2ψ]+ωa2+Λωexp[−2ψ]ζmρm,(24)where H≡˙a/a is the Hubble expansion rate.We can rewrite this more simply as(˙ψa3˙)=N exp[−2ψ](25) where N is a positive constant deﬁned byN=−2ζmρm a3matched approximations.We shall consider the form of the solutions to these equations when the universe is successively dominated by the kinetic energy of the scalarﬁeldψ,pressure-free matter,radiation,negative spatial curvature, and positive cosmological constant.Our analytic expressions are checked by numerical solutions of(23)and(24).3.2Observational implicationsThere are a number of conclusions that can be drawn from the study of the simple BSBM models withζm<0.These models give a goodﬁt to the varying αimplied by the QSO data of refs.[2,3].There is just a single parameter to ﬁt and this is given by the choice−ζmﬁxed to the value given in eq.(29)using a bestﬁt of the theories cosmological model to the QSO observations of refs.[2,3].Other predictions of such WEP violations have also been made in refs.[41,42,43,44].The observational upper bound on this parameter is just an order of magnitude larger,at10−12, but space-based tests planned for the STEP mission are expected to achieve a sensitivity of order10−18and will provide a completely independent check on theories of time-varying e andα.This is an exciting prospect for the future. 3.3The nature of the Friedmann solutionsThe cosmological behaviour of the solutions to these equations was studied by us in detail,both analytically and numerically in refs.[22,21,20,24], [35].Typically,the variation inαdoes not have a signiﬁcant eﬀect on the evolution of the scale factor at late times although the cosmological expansion does signiﬁcantly aﬀect the evolution ofα.The evolution ofαis summarised as follows:During the radiation era a(t)∼t1/2andαis constant in universes with our entropy per baryon and present value ofαlike our own.It increases in the dust era,where a(t)∼t2/3.The increase inαhowever,is very slow with a late-time solution forψproportional to1This type of behaviour can also be found in the presence of time-varying G.If a BD dust universe is exactlyﬂat(k=0)then G will continue to fall forever.Only if there is negative curvature will the evolution of G eventually be turned oﬀand the expansion asymptote to the Milne behaviour with a=t and G→constant.Again,without the small deviation fromﬂatness the strength of gravity would ultimately become too weak for the existence of stars and planets and the universe would become biologically inhospitable,if not uninhabitable.There have been several studies,following Carter,[46]and Tryon[47],of the need for life-supporting universes to expand close to the’ﬂat’Einstein de Sitter trajectory for long periods of time.This ensures that the universe cannot collapse back to high density before galaxies,stars,and biochemical elements can form by gravitational instability,or expand too fast for stars and galaxies to form by gravitational instability[48,7].Likewise,it was pointed out by Barrow and Tipler,[7]that there are similar anthropic restrictions on the magnitude of any cosmological constant,Λ.If it is too large in magnitude it will either precipitate premature collapse back to high density(ifΛ<0)or prevent the gravitational condensation of any stars and galaxies(ifΛ>0).Thus existing studies provide anthropic reasons why we can expect to live in an old universe that is neither too far fromﬂatness nor dominated by a much stronger cosmological constant than observed(|Λ|≤10|Λobs|).Inﬂationary universe models provide a possible theoretical explanation for proximity toﬂatness but no explanation for the smallness of the cosmologi-cal constant.Varying speed of light theories[49,31,50,51,52]oﬀer possible explanations for proximity toﬂatness and smallness of a classical cosmologi-cal constant(but not necessarily for one induced by vacuum corrections in the early universe).We have shown that if we enlarge our cosmological theory to accommodate variations in some traditional constants then it appears to be an-thropically disadvantageous for a universe to lie too close toﬂatness or for the cosmological constant to be too close to zero.This conclusion arises because of the coupling between time-variations in constants likeαand the curvature or Λ,which control the expansion of the universe.The onset of a period ofΛor curvature domination has the property of dynamically stabilising the constants, thereby creating favourable conditions for the emergence of structures.This point has been missed in previous studies because they have never combined the issues ofΛandﬂatness and the issue of the values of constants.By coupling these two types of anthropic considerations weﬁnd that too small a value ofΛor the spatial curvature can be as poisonous for life as too much.Universes like those described above,with increasingα(t),lead inexorably to an epoch where αis too large for the existence of atoms,molecules,and stars to be possible.Surprisingly,there has been almost no consideration of habitability in cos-mologies with time-varying constants since Haldane’s discussions[5]of the bio-logical consequences of Milne’s bimetric theory of gravity.Since then,attention has focussed upon the consequences of universes in which the constants are dif-ferent but still constant.Those cosmologies with varying constants that have been studied have not considered the eﬀects of curvature orΛdomination on the variation of constants and have generally considered power-law variation to12hold for all times.The examples described here show that this restriction has prevented a full appreciation of the coupling between the expansion dynamics of the universe and the values of the constants that deﬁne the course of local physical processes within it.Our discussion of a theory with varyingαshows for theﬁrst time a possible reason why the3-curvature of universes and the value of any cosmological constant may need to be bounded below in order that the universe permit atomic life to exist for a signiﬁcant period.Previous an-thropic arguments have shown that the spatial curvature of the universe and the value of the cosmological constant must be bounded above in order for life-supporting environments(stars)to develop.We note that the lower bounds discussed here are more fundamental than these upper bounds because they de-rive from changes inαwhich have direct consequences for biochemistry whereas the upper bounds just constrain the formation of astrophysical environments by gravitational instability.Taken together,these arguments suggest that within an ensemble of all possible worlds whereαand G are time variables,there might only be aﬁnite interval of non-zero values of the curvature and cosmological constant contributions to the dynamics that both allow galaxies and stars to form and their biochemical products to persist.3.4The role of inhomogeneitiesWe can also detect where and how we might expect spatial variations to arise in a fuller description.Aside from the complexities of the full inhomogeneous cosmological solution for the formation of galaxies,stars,and planets,we can isolate non-uniformities that enter through the constant parameter N which dictates the form and time-evolution of a(t)andα(t).First we see that N is proportional to the density of electromagnetically charged matter in the uni-verse.This will possess some spatial variation and is of order10−5on large scales.More signiﬁcant though is the variation of the baryonic content of the CDM density with scale.We need the CDM to be dominated by matter with magnetic charge(but see Bekenstein).This can be the case on large scale but we know that the dark matter becomes dominated by baryons(therefore with ζ>0)locally.Hence,there is expected to be a very signiﬁcant spatial variation ofζwith scale,including a change of sign,which will feed into the variation of α.3.5General properties of the evolution of alpha and G The evolution equation forψ(t)has a number of simple but important proper-ties.Since N>0the right-hand side or eq.(25)must be positive.This means that linearisations of this equation are dangerous and give rise to linearisation instabilities unless attention is conﬁned to the regimeψ<<1.In general the positivity property means that there can be no oscillations ofψorαin time in solutions of this equation.This follows from the required positivity of(˙ψa3˙),13which means thatψcannot have a maximum.The possible cosmological evolu-tions forψandαare decrease to a minimum followed by a monotonic increase, monotonic decrease,or monotonic increase.This conclusion holds independently of the value of k in the Friedmann equation.This has one very important con-sequence.It means that the asymptotic monotonic non-decrease ofαfound in ourﬂat and open universes will still occur in closed universes.There cannot be a sudden change in the evolution ofαwhen the universe starts to collapse. This also means that if we model spherical overdensities by closed universes embedded in aﬂat background then the evolution ofα(t)in the overdensities will be very similar to that in theﬂat background even when the overdensities collapse to form bound’clusters’.This has the important implication that such an inhomogeneous universe will not end up with very diﬀerent values ofαand ˙αin inside and outside the bound inhomogeneities.This argument can also be applied to the evolution ofφand G in BD theory. Consider the case of dust(p=0).The combination(˙φa3˙)must now be positive and soφcannot have a maximum and G cannot have a minimum regardless of the sign of the curvature parameter k.In particular,G(t)cannot oscillate. Again,this property acts as a safeguard on the divergent evolution of G inside and outside overdensities.4The Second LawThere has been considerable recent discussion[53,54]about the equivalence of models of the variation of diﬀerent dimensional’constants’of Nature.In particular,it has been suggested that consideration of the second law of black hole thermodynamics distinguishes,say,variations of e from variations of c and that some of these variations could be ruled out because they bring about a decrease in time of the Bekenstein-Hawking entropy of a charged black hole. Others have argued that no such distinction is operationally possible.However, we believe that the most crucial factor has been missed in this discussion.In theories which generalise general relativity by allowing traditional constants (like G or e)to vary the black hole solutions with event horizons are particular solutions of the theory in which the constant concerned is a constant.When the constant varies the black hole solution no longer exists and there is no longer any black hole thermodynamics to constrain the variation.The situation is very clear in the simple case of a Schwarzschild black hole in Brans Dicke theory.We know from the work of Hawking[55]that the black hole solutions are the same as those in general relativity.Thus Schwarzschild is aφ˜G−1=constant solution of the Brans-Dickeﬁeld equations.The entropy of this black hole isS bh˜GM2.If we were to apply the second law to this formula it would appear to say that all cosmological solutions in which G falls with time are ruled out.However,this would not be a correct deduction(which is fortunate because we see from eq.(10)that essentially all Brans-Dicke cosmologies have such behaviour)because14φand G are constant on the Schwarzschild horizon.If we allow variation of G then the solution turns into a naked singularity and the thermodynamic relations no longer exist.Thus one cannot at present use considerations of black hole thermodynamics to constrain or distinguish the time or space variation of constants of Nature by simply’writing in’time variations into the formulae that deﬁne the black hole when these constants do not vary.Acknowledgements I would like to thank my collaborators Jo˜a o Magueijo, H˚avard Sandvik,John Webb,Michael Murphy and David Mota for their essen-tial contributions to the work described here.I would also like to thanks Bruce Bassett,Thibault Damour,Paul Davies,Tamara Davies,Carlos Martins,John Moﬀat and Cliﬀord Will for discussions.References[1]J.D.Barrow,The Constants of Nature:from alpha to omega,JonathanCape,London(2002).[2]M.Murphy,J.Webb,V.Flambaum,V.Dzuba,C.Churchill,J.Prochaska,A.Wolfe,MNRAS,327,1208(2001)[3]J.K.Webb,V.V.Flambaum,C.W.Churchill,M.J.Drinkwater J.D.Bar-row,Phys.Rev.Lett.82,884(1999);J.K.Webb,M.T.Murphy,V.V.Flambaum,V.A.Dzuba,J.D.Barrow,C.W.Churchill,J.X.Prochaska,A.M.Wolfe,Phys.Rev.Lett.87,091301(2001).[4]ne,Relativity,Gravitation and World Structure,Clarendon,Ox-ford,(1935).[5]J.B.S.Haldane,Nature139,1002(1937)and158,555(1944)and article inNew Biology,No.16,eds.M.L.Johnson et al,Penguin,London(1955).[6]H.Weyl,Ann.Physik59,129(1919).[7]J.D.Barrow and F.J.Tipler,The Anthropic Cosmological Principle,OxfordUP,Oxford(1986).[8]P.A.M.Dirac,Nature139,323(1937).[9]E.Teller,Phys.Rev.73,801(1948).[10]R.H.Dicke,Rev.Mod.Phys.29,355(1957)and Nature192,440(1961).[11]C.Brans and R.H.Dicke,Phys.Rev.124,924(1961).[12]J.D.Barrow,Mon.Not.R.astr.Soc.,282,1397(1996).[13]J.D.Barrow,in Proc.Erice Summer School Current Topics in Astrofunda-mental Physics:Primordial Cosmology,pp.269-305,ed.N.Sanchez(1997), gr-qc/9711084.15。

语法1

1.Human mortality, whilst consisting of unpredictable individual events, has a statisticalregularity when averaged across a large group. This makes possible a whole host ofproducts, of which the annuity is one. The price of an annuity paying a fixed regular income for life is based upon the statistical life expectancy of the purchaser at the time the annuity is to begin. The company selling the annuity will benefit from all those customers that die earlier than predicted, while customers are attracted by the prospect of guaranteed income for as long as they live. Annuities have the disadvantage that the capital invested isunrecoverable (i.e. upon the death of annuitant nothing is left for the heirs), but that factalso enables annuities to guarantee higher payments than could be obtained if the samesum of money were invested at interest.●The heirs of a person who buy an annuity tend to be against the purchase. C●Essentially, the purchaser of an annuity is gambling that they will live long enough toreceive a good return on their investment. C●Annuity returns are generally similar to returns from investing the money in aninterest bearing accounts. B2.In casual language, the terms theory and model are often used interchangeably. From atechnical point of view there is an important difference. Theories provide a generalframework, but because of the generality of the specification, a theory cannot be shownto be useful or useless until it is fully specified in the form of a model. A model, on theother hand, needs by definition to be formulated within the concepts, along with a set ofassumptions about the concepts and their relationships. The appropriateness of a modelmust then be evaluated with respect to a particular set of test data. The evaluation maybe done by conducting a suitably designed set of empirical investigations, by rationalinspection of the model assumptions in relation to the test data, or ideally both.In the strict sense, all models provide incomplete representations of the data to which they to fitted. Therefore the meaningful question is not whether a model is correct or incorrect, but rather whether the model fits the data well enough to be useful in guiding the process.Statistical evidence and judgment play important roles in answering that question.●It is more meaningful to look at the practical utility of a model than its absolute veracity.T●Most people fail to understand the difference between a theory and a model. C● A model can exist in the absence of a theory. Bmunication technologies are far from equivalent. A recent study comparing honestyacross a range of different media revealed that people were twice as likely to tell lieswhen using the phone than when communicating via e-mail. It had previously beenassumed that people would be more inclined to fabricate the truth when using e-mail,due to the remoteness of the interaction making people more comfortable aboutdeceiving others. On the contrary, it seems that anxiety over the accountability （有义务有责任的）afforded by the recording of e-mail exchanges induces greater truthfulness.However, the research also noted that people are much more likely to be rude orinsulting over e-mail, outweighing any benefits of increased honesty!●An implication of the study is that if telephone conversations are recorded andpeople are aware of this fact, they are likely to be more truthful over the phone. T●People are unconcerned about the repercussion（影响反响） of e-mail untruths. F●It had been assumed that people would communicate more honestly when using e-mail than when using the telephone. F4.There is often considerable scientific disagreement both about available reserves of naturalresources and about the extent of environmental damage caused by particular pollutants.Even where the scientific evidence is incontrovertible 无可争议的证据. There may bepolitical conflict, based on different vested interests, over the degree to which particularenvironmental controls should be accepted. Governments may, for example, refrain（节制） from introducing effective control if they fear these will adversely affect companyprofitability or jobs, even where the environmental cost of not introducing controls areconsiderable.●There is always scientific debate around the facts regarding the reserves ofnatural resources. T●Very rarely is there conflict over the degree to which particular environmentalcontrols should be accepted. F●Parties with a vested interest （既得利益）are more influenced by politics thanscience when deciding whether to implement environmental controls. T/C5.Whilst high visibility crime such as night-time drunken disturbance has increased, totalurban and rural crime, both reported and unreported, has fallen over the last two years,yet paradoxically people feel less safe, believing that the converse is the case. This fall incrime has coincided with a drop in the number of police officer on the street. A citizen’sfear of crime seems not to be a matter of reality at all- the visibility of law enforcementofficials has a greater impact on their view of reality than hard facts.●Reducing the number of police officer has led to a reduction in crime. C●Crime statistics support popular belief about the level of crime. F●People feel safer when there are more police on the street. C/A6.There is no task more difficult than that of ensuring the education of children in modernsociety. Not only school, but also teachers and their roles have changed out of allrecognition in the past few decades, thanks to the impact on teaching institutions byindoctrinating, and indoctrinated, reformist intellectuals bearing revolutionary ideas. Tothe perpetual indiscipline （持续无纪律）of youth has now been added the indisciplineof parents, many of whom interpret any reports of wrongdoing in school on the part oftheir offspring as a personal affront（人身攻击）, or as the manifestation of the malice（厌恶） of teachers. As for the teachers themselves, whilst many are respectable andlearned men and women, who view it as their vocation to induct their charges into acivilization and a way of behaving, others attempt to influence youth merely to further their political or ideological ends.●Some of those working in education have their own hidden agendas. T●Teacher with revolutionary ideas will attempt to influence their pupils for theirown political ends. C●Some teachers who report children of wrongdoing do so because of malice,rather than nay legitimate reason. Cst week, the competition commission outlined two packages to regulate the sale ofextended product warranties, which provide repair/replacement for faulty goodsbeyond the manufacturer’s original guarantee. Whilst warranty sa les are currentlyhighly profitable, with some retailers attributing up to ¾ of their profits to this income stream, they are also criticized for offering poor value for money due to obscure clauses （模棱两可的条款）, which restrict payment in many, but the most unlikely claimscenarios. The first package-to ban retailers selling a full warranty on the day ofpurchase was condemned by all as draconian（严厉的）-whilst the other, rather milder, option of forcing retailers to provide full information on warranty exclusions and anobligatory 60–day “cool-off” period for customers, received a more balanced hearing.Because no one believes that the first option will ever be implemented, investors and analysts have focu sed more closely on the implication of the “milder” package. In arecent leaked research note, one analyst suggested that the implementation of thereform in the second package would place a staff-training burden on the retailer,which would lead to a significant increase in the cost of warranty sales, and apredicted 20% fall in actual sales.●“Cool-off” periods are not currently offered by companies selling productwarranties. T●It is likely that neither package will be implemented. C●Preventing retailers from selling warranties on the day of purchase of a productwas felt to be too severe a restriction. T8.All scientific knowledge is provisional（暂时的）. Everything that science knows, even themost mundane（世俗的） facts and long-established theories, is subject to re-examination as new information comes in. the latest data and ideas are scrutinized the most. Some recantations（取消改变） will be unavoidable, but this is not a weakness of science, but rather its strength. No endeavor rivals science in its incremental progresstowards a more complete understanding of the observable universe.●Science improves understanding on the basis of leaving unchallenged thosetheories that appear to work. F●Some facts in science cannot be challenged if any progress is to be made.F●That which is not observable cannot be part of the domain of science. C9.The Statute on workplace safety requires that an employer should ensure, so far as isreasonably practicable, the health, safety and welfare at work of all full and part timeemployees, and also those not in direct employment who may be affected by acts oromissions at work. However, it is also the duty of employees to take reasonable care fortheir own health and safety and also that of other persons who may be affected by their acts or omissions at work, for example by complying with all notices on health and safety thatare posted.●If a workplace visitor is hurt due to an act of negligence by an employee then theemployee may be held solely responsible. F●An employer has responsibility for the safety of visitors to his factory. A●Employees have negligible可忽视的 responsibility for workplace health and safety. F10.Today’s historians aim to construct a record of human activities and to use this record toachieve a more profound understanding of humanity. This conception of their task is quite recent, dating from the development from 18th and early 19th centuries of scientific history, and cultivated largely by professional historians who adopted the assumption that the study of natural, inevitable human activity. Before the late 18th century, history was taught invirtually（actually） no schools, and it did not attempt to provide an interpretation ofhuman life as a whole. This is more appropriately the function of religion, of philosophy, or even perhaps of poetry.●That which constitutes the study of history has changed over time. T●Professional historians did not exist before 18th century. C●In the 17th century, history would not have been thought of as a way of understandinghumanity. A11.Whilst having similar effects on employees, there tend to be major difference between amerger and an acquisition. In an acquisition, power is substantially assumed by the newparent company. Change is often swift and brutal as the acquirer imposes its own controlsystems and financial restraints(抑制). Parties to a merger are likely to be evenly matched in terms of size, and the power and cultural dynamics of the combination are moreambiguous, integration is a more drawn out 拉长process.During an acquisition, there is often more overt(obvious) conflict and resistance and a sense of powerlessness. In mergers, because of the prolonged period between the initialannouncement and full integration, uncertainty and anxiety continue for a much longer time as the organization remains in a state of limbo.灰色地带●There tends to be a major power difference between parties in an acquisition. T●Mergers and acquisition tend to have distinctly different impacts on employees. F●Mergers yield a shorter period of anxiety and uncertainty amongst employees. F12.Management is, in effect, the catalyst 催化剂 that is essential for converting the resourcesand raw material inputs of the operation into valued outputs and, in the process, ensuring that stakeholder needs are satisfied. Managers represent the critical factor, whicheconomists refer to as “enterprise”, without which the other factors (land, labor and capital) cannot function. Managers are effectively the custodians（保管人）of the organization’sresource, responsible for deciding what the resources should be used for, how best to use them, and to which customers the outputs should be targeted.●Stakeholder needs are best served through the creation of valued outputs. C●Management has at least two major but different responsibilities. A●Managers must decide how best to handle all the resources at their disposal. A13.There is no doubt that vegetarian food can be healthier than a traditional diet（饮食）–indeed, research has demonstrated that vegetarians are less likely to suffer from heartdisease and obesity than those who eat meat. One long-standing concern about a vegetarian lifestyle is the risk of failing to take in enough protein. However, historical calculations as to the amount of protein needed for a healthy lifestyle have recently been shown tooverestimate the quantities needed, and if vegetarian select their food carefully they should be able to meet their protein needs.● A balanced diet is more likely to promote health than any particular food or food groupin isolation. B●Too much protein in the diet can lead to heart disease. C●Over time the recommendations as to what constitutes a healthy balanced diet havechanged. T14.Water, the most common liquid used for cleaning, has a property called surface tension.表面张力 Molecules in the body of the water are surrounded by other molecules, but at thesurface a “tension” is created as molecules are only surrounded by other molecules on the waterside. This tension inhibits the cleaning process, as it slows the wetting of surface due to tension causing the water to bead up（聚合）. This is where water droplets hold theirshape and do not spread. For effective cleaning to take place “surface tension” must bereduced so that water can spread. Surface-active agents表面活化剂, or surfactants, arechemicals, which are able to do this effectively.●Surface-active agents, or surfactants, are only used for cleaning. C●Water is the only known liquid used for cleaning. F●If surfactant chemicals are added to water when cleaning a surface, surface tension willoccur. F●The molecules on the waterside hinder the cleaning process. F15.The biggest risk facing the world’s insurance companies is possibly the rapid change nowtaking place within their own ranks. Sluggish growth in core markets and intense pricecompetition, coupled with shifting patterns of customer demand and the rising cost of losses, are threatening to overwhelm those too slow to react.●Insurance companies are experiencing a boom in their core markets. F●Insurance companies are competing to provide best prices to customers. T●Insurance companies are coping well with increased price competition and rising losses.C16.Short-sightedness is to a large extent inherited, its incidence varies from one family toanother. The reason behind the link between the common incidence of short-sightednessand high intelligence is unclear. Previous generations thought that eyes could becomestrained by years spent poring over研读 books, but a few decades ago the popular medical view was that short-sighted people gravitated被吸引 towards the library because theyfound it hard to excel at sports. Recently there has been partial support for a theory thathigh intelligence and short-sightedness may, in fact, be part of a genetic package.●The genetic link between intelligence and short-sightedness has recently beendisproven. F●People from all families stand at an equal chance of being short-sighted. F●Intelligence is to a large extent inherited C17.The cosmic microwave background (CMB) radiation is the afterglow夕照 from the Big Bang,and weak as it may be today, these primeval 初期microwaves hold valuable informationabout fundamental properties of the early universe. Slight differences, or anisotropies异向性， in the brightness and polarization极化 of the CMB reveal clues about the nature of thepolarized microwaves and the cosmological polarization must thus be measured at different wavelengths so as to isolate them from foreground signals前景近景.●The anisotropies of the CMB show solely that the primordial plasma was not uniform. F●The polarization of cosmic microwaves is measured at different wavelength so as toseparate the foreground from the background signals. T●Through studying the cosmological microwaves, one may learn about the forces ofgravity in the early universe. T18.Internet experts are warning of a new multitude of extremely dangerous computer virusesthat have recently been causing devastation and could potentially cripple使瘫痪 entireglobal computer systems. These viruses can replicate thousands of copies within hours and are capable of extirpating破除 security software that, in turn, enables hackers toappropriate control of the machines. Criminal gangs犯罪团伙 can then establish bankaccounts using stolen identities, sabotage破坏a company’s computer system and extort敲诈 money for its restoration恢复, and sell computers that have been interfered with on the black market. Computer users are often advised to refrain避免 from opening suspiciousprogram attached to the emails and to continually update their security software.●Internet experts are advising computer users to replace their software if they suspect ithas been tampered with篡改. C19.For most people, any reference to hypnosis 催眠brings to mind images of individualsinvolved in amusing, and often out of character, behavior. However, hypnosis is also a topic of scientific research. Research by scientists over the last few decades has revealed ways in which memory processes, and processes involved in pain perception can be changed using hypnosis. It has also been found that hypnotic suggestions can regulate activity inidentifiable sections of the brain and can contribute to the effective management ofcognitive conflict.认知冲突。

你如何看待统计学英文作文

你如何看待统计学英文作文英文：As for me, I think statistics is a very important subject. It helps us to make sense of the world around us by organizing and analyzing data. For example, in my job as a marketing analyst, I use statistics to understand consumer behavior and make predictions about future trends. Without statistics, I would just be guessing, but with it, I can make informed decisions that benefit my company.I also believe that statistics is a crucial part of scientific research. When conducting experiments, it's essential to use statistical methods to analyze the results and draw meaningful conclusions. For instance, in a recent study I was involved in, we used statistical tests to determine whether a new drug was effective in treating a certain disease. The results were clear and convincing, thanks to the rigorous statistical analysis we employed.In addition, statistics is also widely used in everyday life. Whether it's evaluating the performance of a sports team, tracking sales figures for a small business, or understanding the risks and benefits of a medical treatment, statistics is everywhere. Personally, I find it fascinating how statistics can reveal patterns and trends that mightnot be obvious at first glance.中文：对我来说，我觉得统计学是一个非常重要的学科。

审计学：一种整合方法阿伦斯英文版第12版课后答案Chapter15SolutionsManual

审计学：⼀种整合⽅法阿伦斯英⽂版第12版课后答案Chapter15SolutionsManualChapter 15Audit Sampling for Tests of Controls andSubstantive Tests of TransactionsReview Questions15-1 A representative sample is one in which the characteristics of interest for the sample are approximately the same as for the population (that is, the sample accurately represents the total population). If the population contains significant misstatements, but the sample is practically free of misstatements, the sample is nonrepresentative, which is likely to result in an improper audit decision. The auditor can never know for sure whether he or she has a representative sample because the entire population is ordinarily not tested, but certain things, such as the use of random selection, can increase the likelihood of a representative sample.15-2Statistical sampling is the use of mathematical measurement techniques to calculate formal statistical results. The auditor therefore quantifies sampling risk when statistical sampling is used. In nonstatistical sampling, the auditor does not quantify sampling risk. Instead, conclusions are reached about populations on a more judgmental basis.For both statistical and nonstatistical methods, the three main parts are:1. Plan the sample2. Select the sample and perform the tests3. Evaluate the results15-3In replacement sampling, an element in the population can be included in the sample more than once if the random number corresponding to that element is selected more than once. In nonreplacement sampling, an element can be included only once. If the random number corresponding to an element is selected more than once, it is simply treated as a discard the second time. Although both selection approaches are consistent with sound statistical theory, auditors rarely use replacement sampling; it seems more intuitively satisfying to auditors to include an item only once.15-4 A simple random sample is one in which every possible combination of elements in the population has an equal chance of selection. Two methods of simple random selection are use of a random number table, and use of the computer to generate random numbers. Auditors most often use the computer to generate random numbers because it saves time, reduces the likelihood of error, and provides automatic documentation of the sample selected.15-5In systematic sampling, the auditor calculates an interval and then methodically selects the items for the sample based on the size of the interval. The interval is set by dividing the population size by the number of sample items desired.To select 35 numbers from a population of 1,750, the auditor divides 35 into 1,750 and gets an interval of 50. He or she then selects a random number between 0 and 49. Assume the auditor chooses 17. The first item is the number 17. The next is 67, then 117, 167, and so on.The advantage of systematic sampling is its ease of use. In most populations a systematic sample can be drawn quickly, the approach automatically puts the numbers in sequential order and documentation is easy.A major problem with the use of systematic sampling is the possibility of bias. Because of the way systematic samples are selected, once the first item in the sample is selected, other items are chosen automatically. This causes no problems if the characteristics of interest, such as control deviations, are distributed randomly throughout the population; however, in many cases they are not. If all items of a certain type are processed at certain times of the month or with the use of certain document numbers, a systematically drawn sample has a higher likelihood of failing to obtain a representative sample. This shortcoming is sufficiently serious that some CPA firms prohibit the use of systematic sampling. 15-6The purpose of using nonstatistical sampling for tests of controls and substantive tests of transactions is to estimate the proportion of items in a population containing a characteristic or attribute of interest. The auditor is ordinarily interested in determining internal control deviations or monetary misstatements for tests of controls and substantive tests of transactions.15-7 A block sample is the selection of several items in sequence. Once the first item in the block is selected, the remainder of the block is chosen automatically. Thus, to select 5 blocks of 20 sales invoices, one would select one invoice and the block would be that invoice plus the next 19 entries. This procedure would be repeated 4 other times.15-8 The terms below are defined as follows:15-8 (continued)15-9The sampling unit is the population item from which the auditor selects sample items. The major consideration in defining the sampling unit is making it consistent with the objectives of the audit tests. Thus, the definition of the population and the planned audit procedures usually dictate the appropriate sampling unit.The sampling unit for verifying the occurrence of recorded sales would be the entries in the sales journal since this is the document the auditor wishes to validate. The sampling unit for testing the possibility of omitted sales is the shipping document from which sales are recorded because the failure to bill a shipment is the exception condition of interest to the auditor.15-10 The tolerable exception rate (TER) represents the exception rate that the auditor will permit in the population and still be willing to use the assessed control risk and/or the amount of monetary misstatements in the transactions established during planning. TER is determined by choice of the auditor on the basis of his or her professional judgment.The computed upper exception rate (CUER) is the highest estimated exception rate in the population, at a given ARACR. For nonstatistical sampling, CUER is determined by adding an estimate of sampling error to the SER (sample exception rate). For statistical sampling, CUER is determined by using a statistical sampling table after the auditor has completed the audit testing and therefore knows the number of exceptions in the sample.15-11 Sampling error is an inherent part of sampling that results from testing less than the entire population. Sampling error simply means that the sample is not perfectly representative of the entire population.Nonsampling error occurs when audit tests do not uncover errors that exist in the sample. Nonsampling error can result from:1. The auditor's failure to recognize exceptions, or2. Inappropriate or ineffective audit procedures.There are two ways to reduce sampling risk:1. Increase sample size.2. Use an appropriate method of selecting sample items from thepopulation.Careful design of audit procedures and proper supervision and review are ways to reduce nonsampling risk.15-12 An attribute is the definition of the characteristic being tested and the exception conditions whenever audit sampling is used. The attributes of interest are determined directly from the audit program.15-13 An attribute is the characteristic being tested for in a population. An exception occurs when the attribute being tested for is absent. The exception for the audit procedure, the duplicate sales invoice has been initialed indicating the performance of internal verification, is the lack of initials on duplicate sales invoices.15-14 Tolerable exception rate is the result of an auditor's judgment. The suitable TER is a question of materiality and is therefore affected by both the definition and the importance of the attribute in the audit plan.The sample size for a TER of 6% would be smaller than that for a TER of 3%, all other factors being equal.15-15 The appropriate ARACR is a decision the auditor must make using professional judgment. The degree to which the auditor wishes to reduce assessed control risk below the maximum is the major factor determining the auditor's ARACR.The auditor will choose a smaller sample size for an ARACR of 10% than would be used if the risk were 5%, all other factors being equal.15-16 The relationship between sample size and the four factors determining sample size are as follows:a. As the ARACR increases, the required sample size decreases.b. As the population size increases, the required sample size isnormally unchanged, or may increase slightly.c. As the TER increases, the sample size decreases.d. As the EPER increases, the required sample size increases.15-17 In this situation, the SER is 3%, the sample size is 100 and the ARACR is 5%. From the 5% ARACR table (Table 15-9) then, the CUER is 7.6%. This means that the auditor can state with a 5% risk of being wrong that the true population exception rate does not exceed 7.6%.15-18 Analysis of exceptions is the investigation of individual exceptions to determine the cause of the breakdown in internal control. Such analysis is important because by discovering the nature and causes of individual exceptions, the auditor can more effectively evaluate the effectiveness of internal control. The analysis attempts to tell the "why" and "how" of the exceptions after the auditor already knows how many and what types of exceptions have occurred.15-19 When the CUER exceeds the TER, the auditor may do one or more of the following:1. Revise the TER or the ARACR. This alternative should be followed onlywhen the auditor has concluded that the original specifications weretoo conservative, and when he or she is willing to accept the riskassociated with the higher specifications.2. Expand the sample size. This alternative should be followed whenthe auditor expects the additional benefits to exceed the additionalcosts, that is, the auditor believes that the sample tested was notrepresentative of the population.3. Revise assessed control risk upward. This is likely to increasesubstantive procedures. Revising assessed control risk may bedone if 1 or 2 is not practical and additional substantive proceduresare possible.4. Write a letter to management. This action should be done inconjunction with each of the three alternatives above. Managementshould always be informed when its internal controls are notoperating effectively. If a deficiency in internal control is consideredto be a significant deficiency in the design or operation of internalcontrol, professional standards require the auditor to communicatethe significant deficiency to the audit committee or its equivalent inwriting. If the client is a publicly traded company, the auditor mustevaluate the deficiency to determine the impact on the auditor’sreport on internal control over financial reporting. If the deficiency isdeemed to be a material weakness, the auditor’s report on internalcontrol would contain an adverse opinion.15-20 Random (probabilistic) selection is a part of statistical sampling, but it is not, by itself, statistical measurement. To have statistical measurement, it is necessary to mathematically generalize from the sample to the population.Probabilistic selection must be used if the sample is to be evaluated statistically, although it is also acceptable to use probabilistic selection with a nonstatistical evaluation. If nonprobabilistic selection is used, nonstatistical evaluation must be used.15-21 The decisions the auditor must make in using attributes sampling are: What are the objectives of the audit test? Does audit sampling apply?What attributes are to be tested and what exception conditions are identified?What is the population?What is the sampling unit?What should the TER be?What should the ARACR be?What is the EPER?What generalizations can be made from the sample to thepopulation?What are the causes of the individual exceptions?Is the population acceptable?15-21 (continued)In making the above decisions, the following should be considered: The individual situation.Time and budget constraints.The availability of additional substantive procedures.The professional judgment of the auditor.Multiple Choice Questions From CPA Examinations15-22 a. (1) b. (3) c. (2) d. (4)15-23 a. (1) b. (3) c. (4) d. (4)15-24 a. (4) b. (3) c. (1) d. (2)Discussion Questions and Problems15-25a.An example random sampling plan prepared in Excel (P1525.xls) is available on the Companion Website and on the Instructor’s Resource CD-ROM, which is available upon request. The command for selecting the random number can be entered directly onto the spreadsheet, or can be selected from the function menu (math & trig) functions. It may be necessary to add the analysis tool pack to access the RANDBETWEEN function. Once the formula is entered, it can be copied down to select additional random numbers. When a pair of random numbers is required, the formula for the first random number can be entered in the first column, and the formula for the second random number can be entered in the second column.a. First five numbers using systematic selection:Using systematic selection, the definition of the sampling unit for determining the selection interval for population 3 is the total number of lines in the population. The length of the interval is rounded down to ensure that all line numbers selected are within the defined population.15-26a. To test whether shipments have been billed, a sample of warehouse removal slips should be selected and examined to see ifthey have the proper sales invoice attached. The sampling unit willtherefore be the warehouse removal slip.b. Attributes sampling method: Assuming the auditor is willing to accept a TER of 3% at a 10% ARACR, expecting no exceptions in the sample, the appropriate sample size would be 76, determined from Table 15-8.Nonstatistical sampling method: There is no one right answer to this question because the sample size is determined using professional judgment. Due to the relatively small TER (3%), the sample size should not be small. It will most likely be similar in size to the sample chosen by the statistical method.c. Systematic sample selection:22839 = Population size of warehouse removal slips(37521-14682).76 = Sample size using statistical sampling (students’answers will vary if nonstatistical sampling wasused in part b.300 = Interval (22839/76) if statistical sampling is used (students’ answers will vary if nonstatisticalsampling was used in part b).14825 = Random starting point.Select warehouse removal slip 14825 and every 300th warehouse removal slip after (15125, 15425, etc.)Computer generation of random numbers using Excel (P1526.xls): =RANDBETWEEN(14682,37521)The command for selecting the random number can be entered directly onto the spreadsheet, or can be selected from the function menu (math & trig) functions. It may be necessary to add the analysis tool pack to access the RANDBETWEEN function. Once the formula is entered, it can be copied down to select additional random numbers.d. Other audit procedures that could be performed are:1. Test extensions on attached sales invoices for clerical accuracy. (Accuracy)2. Test time delay between warehouse removal slip date and billing date for timeliness of billing. (Timing)3. Trace entries into perpetual inventory records to determinethat inventory is properly relieved for shipments. (Postingand summarization)15-26 (continued)e. The test performed in part c cannot be used to test for occurrenceof sales because the auditor already knows that inventory wasshipped for these sales. To test for occurrence of sales, the salesinvoice entry in the sales journal is the sampling unit. Since thesales invoice numbers are not identical to the warehouse removalslips it would be improper to use the same sample.15-27a. It would be appropriate to use attributes sampling for all audit procedures except audit procedure 1. Procedure 1 is an analyticalprocedure for which the auditor is doing a 100% review of the entirecash receipts journal.b. The appropriate sampling unit for audit procedures 2-5 is a line item,or the date the prelisting of cash receipts is prepared. The primaryemphasis in the test is the completeness objective and auditprocedure 2 indicates there is a prelisting of cash receipts. All otherprocedures can be performed efficiently and effectively by using theprelisting.c. The attributes for testing are as follows:d. The sample sizes for each attribute are as follows:15-28a. Because the sample sizes under nonstatistical sampling are determined using auditor judgment, students’ answers to thisquestion will vary. They will most likely be similar to the samplesizes chosen using attributes sampling in part b. The importantpoint to remember is that the sample sizes chosen should reflectthe changes in the four factors (ARACR, TER, EPER, andpopulation size). The sample sizes should have fairly predictablerelationships, given the changes in the four factors. The followingreflects some of the relationships that should exist in student’ssample size decisions:SAMPLE SIZE EXPLANATION1. 90 Given2. > Column 1 Decrease in ARACR3. > Column 2 Decrease in TER4. > Column 1 Decrease in ARACR (column 4 is thesame as column 2, with a smallerpopulation size)5. < Column 1 Increase in TER-EPER6. < Column 5 Decrease in EPER7. > Columns 3 & 4 Decrease in TER-EPERb. Using the attributes sampling table in Table 15-8, the sample sizesfor columns 1-7 are:1. 882. 1273. 1814. 1275. 256. 187. 149c.d. The difference in the sample size for columns 3 and 6 result from the larger ARACR and larger TER in column 6. The extremely large TER is the major factor causing the difference.e. The greatest effect on the sample size is the difference between TER and EPER. For columns 3 and 7, the differences between the TER and EPER were 3% and 2% respectively. Those two also had the highest sample size. Where the difference between TER and EPER was great, such as columns 5 and 6, the required sample size was extremely small.Population size had a relatively small effect on sample size.The difference in population size in columns 2 and 4 was 99,000 items, but the increase in sample size for the larger population was marginal (actually the sample sizes were the same using the attributes sampling table).f. The sample size is referred to as the initial sample size because it is based on an estimate of the SER. The actual sample must be evaluated before it is possible to know whether the sample is sufficiently large to achieve the objectives of the test.15-29 a.* Students’ answers as to whether the allowance for sampling error risk is sufficient will vary, depending on their judgment. However, they should recognize the effect that lower sample sizes have on the allowance for sampling risk in situations 3, 5 and 8.b. Using the attributes sampling table in Table 15-9, the CUERs forcolumns 1-8 are:1. 4.0%2. 4.6%3. 9.2%4. 4.6%5. 6.2%6. 16.4%7. 3.0%8. 11.3%c.d. The factor that appears to have the greatest effect is the number ofexceptions found in the sample compared to sample size. For example, in columns 5 and 6, the increase from 2% to 10% SER dramatically increased the CUER. Population size appears to have the least effect. For example, in columns 2 and 4, the CUER was the same using the attributes sampling table even though the population in column 4 was 10 times larger.e. The CUER represents the results of the actual sample whereas theTER represents what the auditor will allow. They must be compared to determine whether or not the population is acceptable.15-30a. and b. The sample sizes and CUERs are shown in the following table:a. The auditor selected a sample size smaller than that determinedfrom the tables in populations 1 and 3. The effect of selecting asmaller sample size than the initial sample size required from thetable is the increased likelihood of having the CUER exceed theTER. If a larger sample size is selected, the result may be a samplesize larger than needed to satisfy TER. That results in excess auditcost. Ultimately, however, the comparison of CUER to TERdetermines whether the sample size was too large or too small.b. The SER and CUER are shown in columns 4 and 5 in thepreceding table.c. The population results are unacceptable for populations 1, 4, and 6.In each of those cases, the CUER exceeds TER.The auditor's options are to change TER or ARACR, increase the sample size, or perform other substantive tests to determine whether there are actually material misstatements in thepopulation. An increase in sample size may be worthwhile inpopulation 1 because the CUER exceeds TER by only a smallamount. Increasing sample size would not likely result in improvedresults for either population 4 or 6 because the CUER exceedsTER by a large amount.d. Analysis of exceptions is necessary even when the population isacceptable because the auditor wants to determine the nature andcause of all exceptions. If, for example, the auditor determines thata misstatement was intentional, additional action would be requiredeven if the CUER were less than TER.15-30 (Continued)e.15-31 a. The actual allowance for sampling risk is shown in the following table:b. The CUER is higher for attribute 1 than attribute 2 because the sample sizeis smaller for attribute 1, resulting in a larger allowance for sampling risk.c. The CUER is higher for attribute 3 than attribute 1 because the auditorselected a lower ARACR. This resulted in a larger allowance for sampling risk to achieve the lower ARACR.d. If the auditor increases the sample size for attribute 4 by 50 items and findsno additional exceptions, the CUER is 5.1% (sample size of 150 and three exceptions). If the auditor finds one exception in the additional items, the CUER is 6.0% (sample size of 150, four exceptions). With a TER of 6%, the sample results will be acceptable if one or no exceptions are found in the additional 50 items. This would require a lower SER in the additional sample than the SER in the original sample of 3.0 percent. Whether a lower rate of exception is likely in the additional sample depends on the rate of exception the auditor expected in designing the sample, and whether the auditor believe the original sample to be representative.15-32a. The following shows which are exceptions and why:b. It is inappropriate to set a single acceptable tolerable exception rate and estimated population exception rate for the combined exceptions because each attribute has a different significance tothe auditor and should be considered separately in analyzing the results of the test.c. The CUER assuming a 5% ARACR for each attribute and a sample size of 150 is as follows:15-32 (continued)d.*Students’ answers will most likely vary for this attribute.e. For each exception, the auditor should check with the controller todetermine an explanation for the cause. In addition, the appropriateanalysis for each type of exception is as follows:15-33a. Attributes sampling approach: The test of control attribute had a 6% SER and a CUER of 12.9%. The substantive test of transactionsattribute has SER of 0% and a CUER of 4.6%.Nonstatistical sampling approach: As in the attributes samplingapproach, the SERs for the test of control and the substantive testof transactions are 6% and 0%, respectively. Students’ estimates ofthe CUERs for the two tests will vary, but will probably be similar tothe CUERs calculated under the attributes sampling approach.b. Attributes sampling approach: TER is 5%. CUERs are 12.9% and4.6%. Therefore, only the substantive test of transactions resultsare satisfactory.Nonstatistical sampling approach: Because the SER for the test ofcontrol is greater than the TER of 5%, the results are clearly notacceptable. Students’ estimates for CUER for the test of controlshould be greater than the SER of 6%. For the substantive test oftransactions, the SER is 0%. It is unlikely that students will estimateCUER for this test greater than 5%, so the results are acceptablefor the substantive test of transactions.c. If the CUER exceeds the TER, the auditor may:1. Revise the TER if he or she thinks the original specificationswere too conservative.2. Expand the sample size if cost permits.3. Alter the substantive procedures if possible.4. Write a letter to management in conjunction with each of theabove to inform management of a deficiency in their internalcontrols. If the client is a publicly traded company, theauditor must evaluate the deficiency to determine the impacton the auditor’s report on internal control over financialreporting. If the deficiency is deemed to be a materialweakness, the auditor’s report on internal control wouldcontain an adverse opinion.In this case, the auditor has evidence that the test of control procedures are not effective, but no exceptions in the sample resulted because of the breakdown. An expansion of the attributestest does not seem advisable and therefore, the auditor shouldprobably expand confirmation of accounts receivable tests. Inaddition, he or she should write a letter to management to informthem of the control breakdown.d. Although misstatements are more likely when controls are noteffective, control deviations do not necessarily result in actualmisstatements. These control deviations involved a lack ofindication of internal verification of pricing, extensions and footingsof invoices. The deviations will not result in actual errors if pricing,extensions and footings were initially correctly calculated, or if theindividual responsible for internal verification performed theprocedure but did not document that it was performed.e. In this case, we want to find out why some invoices are notinternally verified. Possible reasons are incompetence,carelessness, regular clerk on vacation, etc. It is desirable to isolatethe exceptions to certain clerks, time periods or types of invoices.Case15-34a. Audit sampling could be conveniently used for procedures 3 and 4 since each is to be performed on a sample of the population.b. The most appropriate sampling unit for conducting most of the auditsampling tests is the shipping document because most of the testsare related to procedure 4. Following the instructions of the auditprogram, however, the auditor would use sales journal entries asthe sampling unit for step 3 and shipping document numbers forstep 4. Using shipping document numbers, rather than thedocuments themselves, allows the auditor to test the numericalcontrol over shipping documents, as well as to test for unrecordedsales. The selection of numbers will lead to a sample of actualshipping documents upon which tests will be performed.。

概率论与数理统计英文文献

Introduction to probability theory andmathematical statisticsThe theory of probability and the mathematical statistic are carries on deductive and the induction science to the stochastic phenomenon statistical rule, from the quantity side research stochastic phenomenon statistical regular foundation mathematics discipline, the theory of probability and the mathematical statistic may divide into the theory of probability and the mathematical statistic two branches. The probability uses for the possible size quantity which portrays the random event to occur. Theory of probability main content including classical generally computation, random variable distribution and characteristic numeral and limit theorem and so on. The mathematical statistic is one of mathematics Zhonglian department actually most directly most widespread branches, it introduced an estimate (rectangular method estimate, enormousestimate), the parameter supposition examination, the non-parameter supposition examination, the variance analysis and the multiple regression analysis, the fail-safe analysis and so on the elementary knowledge and the principle, enable the student to have a profound understanding tostatistics principle function. Through this curriculum study, enables the student comprehensively to understand, to grasp the theory of probability and the mathematical statistic thought and the method, grasps basic and the commonly used analysis and the computational method, and can studies in the solution economy and the management practice question using the theory of probability and the mathematical statistic viewpoint and the method.Random phenomenonFrom random phenomenon, in the nature and real life, some things are interrelated and continuous development. In the relationship between each other and developing, according to whether there is a causal relationship, very different can be divided into two categories: one is deterministic phenomenon. This kind of phenomenon is under certain conditions, will lead to certain results. For example, under normal atmospheric pressure, water heated to 100 degrees Celsius, is bound to a boil. This link is belong to the inevitability between things. Usually in natural science is interdisciplinary studies and know the inevitability, seeking this kind of inevitable phenomenon.Another kind is the phenomenon of uncertainty. This kind of phenomenon is under certain conditions, the resultis uncertain. The same workers on the same machine tools, for example, processing a number of the same kind of parts, they are the size of the there will always be a little difference. As another example, under the same conditions, artificial accelerating germination test of wheat varieties, each tree seed germination is also different, there is strength and sooner or later, respectively, and so on. Why in the same situation, will appear this kind of uncertain results? This is because, we say "same conditions" refers to some of the main conditions, in addition to these main conditions, there are many minor conditions and the accidental factor is people can't in advance one by one to grasp. Because of this, in this kind of phenomenon, we can't use the inevitability of cause and effect, the results of individual phenomenon in advance to make sure of the answer. The relationship between things is belong to accidental, this phenomenon is called accidental phenomenon, or a random phenomenon.In nature, in the production, life, random phenomenon is very common, that is to say, there is a lot of random phenomenon. Issue such as: sports lottery of the winning Numbers, the same production line production, the life of the bulb, etc., is a random phenomenon. So we say: randomphenomenon is: under the same conditions, many times the same test or survey the same phenomenon, the results are not identical, and unable to accurately predict the results of the next. Random phenomena in the uncertainties of the results, it is because of some minor, caused by the accidental factors.Random phenomenon on the surface, seems to be messy, there is no regular phenomenon. But practice has proved that if the same kind of a large number of repeated random phenomenon, its overall present certain regularity. A large number of similar random phenomena of this kind of regularity, as we observed increase in the number of the number of times and more obvious. Flip a coin, for example, each throw is difficult to judge on that side, but if repeated many times of toss the coin, it will be more and more clearly find them up is approximately the same number.We call this presented by a large number of similar random phenomena of collective regularity, is called the statistical regularity. Probability theory and mathematical statistics is the study of a large number of similar random phenomena statistical regularity of the mathematical disciplines.The emergence and development of probability theoryProbability theory was created in the 17th century, it is by the development of insurance business, but from the gambler's request, is that mathematicians thought the source of problem in probability theory.As early as in 1654, there was a gambler may tired to the mathematician PASCAL proposes a question troubling him for a long time: "meet two gamblers betting on a number of bureau, who will win the first m innings wins, all bets will be who. But when one of them wins a (a < m), the other won b (b < m) bureau, gambling aborted. Q: how should bets points method is only reasonable?" Who in 1642 invented the world's first mechanical addition of computer.Three years later, in 1657, the Dutch famous astronomy, physics, and a mathematician huygens is trying to solve this problem, the results into a book concerning the calculation of a game of chance, this is the earliest probability theory works.In recent decades, with the vigorous development of science and technology, the application of probability theory to the national economy, industrial and agricultural production and interdisciplinary field. Many of applied mathematics, such as information theory, game theory, queuing theory, cybernetics, etc., are based on the theory of probability.Probability theory and mathematical statistics is a branch of mathematics, random they similar disciplines are closely linked. But should point out that the theory of probability and mathematical statistics, statistical methods are each have their own contain different content.Probability theory, is based on a large number of similar random phenomena statistical regularity, the possibility that a result of random phenomenon to make an objective and scientific judgment, the possibility of its occurrence for this size to make quantitative description; Compare the size of these possibilities, study the contact between them, thus forming a set of mathematical theories and methods.Mathematical statistics - is the application of probability theory to study the phenomenon of large number of random regularity; To through the scientific arrangement of a number of experiments, the statistical method given strict theoretical proof; And determining various methods applied conditions and reliability of the method, the formula, the conclusion and limitations. We can from a set of samples to decide whether can with quite large probability to ensure that a judgment is correct, and can control the probability of error.- is a statistical method provides methods are used in avariety of specific issues, it does not pay attention to the method according to the theory, mathematical reasoning.Should point out that the probability and statistics on the research method has its particularity, and other mathematical subject of the main differences are:First, because the random phenomena statistical regularity is a collective rule, must to present in a large number of similar random phenomena, therefore, observation, experiment, research is the cornerstone of the subject research methods of probability and statistics. But, as a branch of mathematics, it still has the definition of this discipline, axioms, theorems, the definitions and axioms, theorems are derived from the random rule of nature, but these definitions and axioms, theorems is certain, there is no randomness.Second, in the study of probability statistics, using the "by part concluded all" methods of statistical inference. This is because it the object of the research - the range of random phenomenon is very big, at the time of experiment, observation, not all may be unnecessary. But by this part of the data obtained from some conclusions, concluded that the reliability of the conclusion to all the scope.Third, the randomness of the random phenomenon, refers to the experiment, investigation before speaking. After the real results for each test, it can only get the results of the uncertainty of a certain result. When we study this phenomenon, it should be noted before the test can find itself inherent law of this phenomenon.The content of the theory of probabilityProbability theory as a branch of mathematics, it studies the content general include the probability of random events, the regularity of statistical independence and deeper administrative levels.Probability is a quantitative index of the possibility of random events. In independent random events, if an event frequency in all events, in a larger range of stable around a fixed constant. You can think the probability of the incident to the constant. For any event probability value must be between 0 and 1.There is a certain type of random events, it has two characteristics: first, only a finite number of possible results; Second, the results the possibility of the same. Have the characteristics of the two random phenomenon called"classical subscheme".In the objective world, there are a large number of random phenomena, the result of a random phenomenon poses a random event. If the variable is used to describe each random phenomenon as a result, is known as random variables.Random variable has a finite and the infinite, and according to the variable values is usually divided into discrete random variables and the discrete random variable. List all possible values can be according to certain order, such a random variable is called a discrete random variable; If possible values with an interval, unable to make the order list, the random variable is called a discrete random variable.The content of the mathematical statisticsIncluding sampling, optimum line problem of mathematical statistics, hypothesis testing, analysis of variance, correlation analysis, etc. Sampling inspection is to pair through sample investigation, to infer the overall situation. Exactly how much sampling, this is a very important problem, therefore, is produced in the sampling inspection "small sample theory", this is in the case of the sample is small, the analysis judgment theory.Also called curve fitting and optimal line problem. Some problems need to be according to the experience data to find a theoretical distribution curve, so that the whole problem get understanding. But according to what principles and theoretical curve? How to compare out of several different curve in the same issue? Selecting good curve, is how to determine their error? ...... Is belong to the scope of the optimum line issues of mathematical statistics.Hypothesis testing is only at the time of inspection products with mathematical statistical method, first make a hypothesis, according to the result of sampling in reliable to a certain extent, to judge the null hypothesis.Also called deviation analysis, variance analysis is to use the concept of variance to analyze by a handful of experiment can make the judgment.Due to the random phenomenon is abundant in human practical activities, probability and statistics with the development of modern industry and agriculture, modern science and technology and continuous development, which formed many important branch. Such as stochastic process, information theory, experimental design, limit theory, multivariate analysis, etc.译文：概率论和数理统计简介概率论与数理统计是对随机现象的统计规律进行演绎和归纳的科学，从数量侧面研究随机现象的统计规律性的基础数学学科，概率论与数理统计又可分为概率论和数理统计两个分支。

mathematical statistics答案

mathematical statistics答案Mathematical statistics is the application of mathematics to the study of statistics in areas such as data analysis, forecasting, and decision-making. It takes data from various sources, such as surveys, experiments, or observational studies, and uses mathematical principles and models to provide meaningful information about it.The mathematical foundations of statistics are complex, and require the use of probability theory, combinatorics, linear algebra, and other advanced mathematical topics. In addition, many statistical techniques make use of optimization theory, numerical analysis, and computer programming.One of the most important aspects of mathematical statistics is data analysis. This involves collecting, analyzing, andinterpreting data in order to identify patterns and trends, and to make predictions about future outcomes. This data analysis can be done using various techniques, such as linear regression, clustering, and classification.Other uses of mathematical statistics include forecasting, which involves predicting future values of a system based on past data, and decision-making, which involves making decisions based on data and understanding the consequences of those decisions.In the field of education, the use of mathematical statisticsis often required when evaluating student performance or when making decisions about policy and curriculum. This can include analyzing assessment results, predicting student outcomes, or informing administrators about trends in student behavior or motivation.Overall, the application of mathematics to the study of statistics is an important area of research and practice. It is essential in providing meaningful information to decision-makers, and it has implications for almost every industry. As data becomes increasingly more important in today's world, mathematical statistics continues to be a critical component of research and decision-making.。

在统计方面的英语

在统计方面的英语In terms of statistics, there are several key concepts and techniques that are important to understand. These include measures of central tendency, variability, probability, and hypothesis testing. Central tendencyrefers to the typical or average value of a set of data,and can be measured using the mean, median, or mode. Variability, on the other hand, describes the spread or dispersion of the data, and is often measured using the range, variance, or standard deviation. Probability is a measure of the likelihood of a particular event occurring, and is used to make predictions and decisions based on uncertain outcomes. Hypothesis testing is a technique usedto evaluate the strength of evidence in support of a claim about a population parameter.在统计学方面，有几个重要的概念和技术需要理解。

这些包括中心趋势、变异性、概率和假设检验。

中心趋势是指一组数据的典型或平均值，可以用均值、中位数或众数来衡量。

语义分析的一些方法

语义分析的一些方法语义分析的一些方法(上篇)•5040语义分析，本文指运用各种机器学习方法，挖掘与学习文本、图片等的深层次概念。

wikipedia上的解释：In machine learning, semantic analysis of a corpus is the task of building structures that approximate concepts from a large set of documents(or images)。

工作这几年，陆陆续续实践过一些项目，有搜索广告，社交广告，微博广告，品牌广告，内容广告等。

要使我们广告平台效益最大化，首先需要理解用户，Context(将展示广告的上下文)和广告，才能将最合适的广告展示给用户。

而这其中，就离不开对用户，对上下文，对广告的语义分析，由此催生了一些子项目，例如文本语义分析，图片语义理解，语义索引，短串语义关联，用户广告语义匹配等。

接下来我将写一写我所认识的语义分析的一些方法，虽说我们在做的时候，效果导向居多，方法理论理解也许并不深入，不过权当个人知识点总结，有任何不当之处请指正，谢谢。

本文主要由以下四部分组成：文本基本处理，文本语义分析，图片语义分析，语义分析小结。

先讲述文本处理的基本方法，这构成了语义分析的基础。

接着分文本和图片两节讲述各自语义分析的一些方法，值得注意的是，虽说分为两节，但文本和图片在语义分析方法上有很多共通与关联。

最后我们简单介绍下语义分析在广点通“用户广告匹配”上的应用，并展望一下未来的语义分析方法。

1 文本基本处理在讲文本语义分析之前，我们先说下文本基本处理，因为它构成了语义分析的基础。

而文本处理有很多方面，考虑到本文主题，这里只介绍中文分词以及Term Weighting。

1.1 中文分词拿到一段文本后，通常情况下，首先要做分词。

分词的方法一般有如下几种：•基于字符串匹配的分词方法。

此方法按照不同的扫描方式，逐个查找词库进行分词。

maxent原版英文说明

RESM 575 Spatial AnalysisSpring 2010Lab 6 Maximum EntropyAssigned: Monday March 1Due: Monday March 820 pointsThis lab exercise was primarily written by Steven Phillips, Miro Dudik and Rob Schapire, with support from AT&T Labs-Research, Princeton University, and the Center for Biodiversity and Conservation, American Museum of Natural History. This lab exercise is based on their paper and data:Steven J. Phillips, Robert P. Anderson, Robert E. Schapire.Maximum entropy modeling of species geographic distributions.Ecological Modelling, Vol 190/3-4 pp 231-259, 2006.My goal is to give you a basic introduction to use of the MaxEnt program for maximum entropy model ing of species’ geographic distributions.The environmental data consist of climatic and elevational data for South America, together with a potential vegetation layer. The sample species the authors used will be Bradypus variegatus, the brown-throated three-toed sloth.NOTE on the Maxent softwareThe software consists of a jar file, maxent.jar, which can be used on any computer running Java version 1.4 or later. It can be downloaded, along with associated literature, from /~schapire/maxent. If you are using Microsoft Windows (as we assume here), you should also download the file maxent.bat, and save it in the same directory as maxent.jar. The website has a file called “readme.txt”, which contains instructions for installing the program on your computer.The software has already been downloaded and installed on the machines in 317 Percival.First go to the class website and download the maxent-tutorial-data.zip file.Extract it to the c:/temp folder which will create a c:/temp/tutorial-data directory.Find the maxent directory on the c:/ drive of your computer and simply click on the file maxent.bat. The following screen will appear:To perform a run, you need to supply a file containing presence localities (“samples”), a directory containing environmental variables, and an output directory. In our case, the presence loc alities are in the file “c:\temp\tutorial-data\samples\bradypus.csv”, the environmental layers are in the directory “layers”, and the outputs are going to go in the directory “outputs”. You can enter these locations by hand, or browse for them. While browsing for the environmental variables, remember that you are looking for the directory that contains them –you don’t need to browse down to the files in the directory. After entering or browsing for the files for Bradypus, the program looks like this:The file “samples\bradypus.csv” contains the presence localities in .csv format. The first few lines are as follows:species,longitude,latitudebradypus_variegatus,-65.4,-10.3833bradypus_variegatus,-65.3833,-10.3833bradypus_variegatus,-65.1333,-16.8bradypus_variegatus,-63.6667,-17.45bradypus_variegatus,-63.85,-17.4There can be multiple species in the same samples file, in which case more species would appear in the panel, along with Bradypus. Other coordinate systems can be used, other than latitude and longitude, as long as the samples file and environmental layers use the same coordinate system. The “x” coordinate should come before the “y” coordinate in the samples file.The directory “layers” contains a number of ascii raster grids (in ESRI’s .asc format), each of which describes an environmental variable. The grids must all have the same geographic bounds and cell size. MAKE SURE YOUR ASCII FILES HAVE THE .asc EXTENSION One of our variables, “ecoreg”, is a categorical variable describing potential vegetation classes. You must tell the program which variables are categorical, as has been done in the picture above.Doing a runSimply press the “Run” button. A progress monitor describes the steps being taken. After the environmental layers are loaded and some initialization is done, progress towards training of the maxent model is shown like this:The “gain” starts at 0 and increases towards an asymptote during the run. Maxent is a maximum-likelihood method, and what it is generating is a probability distribution over pixels in the grid. Note that it isn’t calculating “probability of occurrence” – its probabilities are typically very small values, as they must sum to 1 over the whole grid. The gain is a measure of the likelihood of the samples; for example, if the gain is 2, it means that the average sample likelihood is exp(2) ≈ 7.4 times higher than that of a random background pixel. The uniform distribution has gain 0, so you can interpret the gain as representing how much better the distribution fits the sample points than the uniform distribution does. The gain is closely related to “deviance”, as used in statistics.The run produces a number of output files, of which the most important is an html file called “bradypus.html”. Part of this file gives pointers to the other outputs, like this:Looking at a predictionTo see what other (more interesting) content there can be in c:\temp\tutorial-data\outpus\bradpus_variegatus.html, we will turn on a couple of options and rerun the model. Press the “Make pictures of predictions” button, then c lick on “Settings”, and type “25” in the “Random test percentage” entry. Lastly, press the “Run” button again. You may have to say “Replace All” for this new run. After the run completes, the file bradypus.html contains this picture:The image uses colors to show prediction strength, with red indicating strong prediction of suitable conditions for the species, yellow indicating weak prediction of suitable conditions, and blue indicating very unsuitable conditions. For Bradypus, we see strong prediction through most of lowland Central America, wet lowland areas of northwesternSouth America, the Amazon basin, Caribean islands, and much of the Atlantic forests in south-eastern Brazil. The file pointed to is an image file (.png) that you can just click on (in Windows) or open in most image processing software.The test points are a random sample taken from the species presence localities. Test data can alternatively be prov ided in a separate file, by typing the name of a “Test sample file” in the Settings panel. The test sample file can have test localities for multiple species. Statistical analysisThe “25” we entered for “random test percentage” told the program to ran domly set aside 25% of the sample records for testing. This allows the program to do some simple statistical analysis. It plots (testing and training) omission against threshold, and predicted area against threshold, as well as the receiver operating curve show below. The area under the ROC curve (AUC) is shown here, and if test data are available, the standard error of the AUC on the test data is given later on in the web page.A second kind of statistical analysis that is automatically done if test data are available is a test of the statistical significance of the prediction, using a binomial test of omission. For Bradypus, this gives:Which variables matter?To get a sense of which variables are most important in the model, we can run a jackknife test, by selecting the “Do jackknife to measure variable important” checkbox . When we press the “Run” button again, a number of models get created. Each variable is excluded in turn, and a model created with the remaining variables. Then a model is created using each variable in isolation. In addition, a model is created using all variables, as before. The results of the jackknife appear in the “bradypus.html” files in three bar charts, and the first of these is shown below.We see that if Maxent uses only pre6190_l1 (average January rainfall) it achieves almost no gain, so that variable is not (by itself) a good predictor of the distribution of Bradypus. On the other hand, October rainfall (pre6190_l10) is a much better predictor. Turning to the lighter blue bars, it appears that no variable has a lot of useful information that is not already contained in the others, as omitting each one in turn did not decrease the training gain much.The bradypus_variegatus.html file has two more jackknife plots, using test gain and AUC in place of training gain. This allows the importance of each variable to be measure both in terms of the model fit on training data, and its predictive ability on test data.How does the prediction depend on the variables?Now press the “Create response curves”, deselect the jackknife option, and rerun the model. This results in the following section being added to the“bradypus_variegatus.html” file:Each of the thumbnail images can be clicked on to get a more detailed plot. Looking at frs6190_ann, we see that the response is highest for frs6190_ann = 0, and is fairly highfor values of frs6190_ann below about 75. Beyond that point, the response drops off sharply, reaching -50 at the top of the variable’s range.So what do the values on the y-axis mean? The maxent model is an exponential model, which means that the probability assigned to a pixel is proportional to the exponential of some additive combination of the variables. The response curve above shows the contribution of frs6190_ann to the exponent. A difference of 50 in the exponent is huge, so the plot for frs6190_ann shows a very strong drop in predicted suitability for large values of the variable.On a technical note, if we are modeling interactions between variables (by using product features) as we are for Bradypus here, then the response curve for one variable will depend on the settings of other variables. In this case, the response curves generated by the program have all other variables set to their mean on the set of presence localities. Note also that if the environmental variables are correlated, as they are here, the response curves can be misleading. If two closely correlated variables have strong response curves that are near opposites of each other, then for most pixels, the combined effect of the two variables may be small. To see how the response curve depends on the other variables in use, try comparing the above picture with the response curve obtained when using only frs6190_ann in the model (by deselecting all other variables).Feature types and response curvesResponse curves allow us to see the difference between different feature types. Deselect the “auto features”, select “Threshold features”, and press the “Run” butto n again. Take a look at the resulting feature profiles –you’ll notice that they are all step functions, like this one for pre6190_l10:If the same run is done using only hinge features, the resulting feature profile looks like this:The outline of the two profiles is similar, but they differ because the different classes of feature types are limited in the shapes of response curves they are capable of modeling. Using all classes together (the default, given enough samples) allows many complex response curves to be accurately modeled.SWD FormatThere is a second input format that can be very useful, especially when your environmental grids are very large. For lack of a better name, it’s called “samples with data”, or just SWD. The SWD version of our Bradypus file, called “bradypus_swd.csv”, starts like this:species,longitude,latitude,cld6190_ann,dtr6190_ann,ecoreg,frs6190_ann,h_dem,pre6190_ann,pre6190_l10,pre6190_l1, pre6190_l4,pre6190_l7,tmn6190_ann,tmp6190_ann,tmx6190_ann,vap6190_annbradypus_variegatus,-65.4,-10.3833,76.0,104.0,10.0,2.0,121.0,46.0,41.0,84.0,54.0,3.0,192.0,266.0,337.0,279.0 bradypus_variegatus,-65.3833,-10.3833,76.0,104.0,10.0,2.0,121.0,46.0,40.0,84.0,54.0,3.0,192.0,266.0,337.0,279.0 bradypus_variegatus,-65.1333,-16.8,57.0,114.0,10.0,1.0,211.0,65.0,56.0,129.0,58.0,34.0,140.0,244.0,321.0,221.0 bradypus_variegatus,-63.6667,-17.45,57.0,112.0,10.0,3.0,363.0,36.0,33.0,71.0,27.0,13.0,135.0,229.0,307.0,202.0 bradypus_variegatus,-63.85,-17.4,57.0,113.0,10.0,3.0,303.0,39.0,35.0,77.0,29.0,15.0,134.0,229.0,306.0,202.0It can be used in place of an ordinary samples file. The difference is only that the program doesn’t need to look in the environmental layers to get values for the variables at the sample points. The environmental layers are thus only used to get “background” pixels – pixels where the species hasn’t necessarily been found. In fact, the background pixels can also be specified in a SWD format file, in which case the “species” column is ignored. The file “background.csv” ha s 10,000 background data points in it. The first few look like this:background,-61.775,6.175,60.0,100.0,10.0,0.0,747.0,55.0,24.0,57.0,45.0,81.0,182.0,239.0,300.0,232.0 background,-66.075,5.325,67.0,116.0,10.0,3.0,1038.0,75.0,16.0,68.0,64.0,145.0,181.0,246.0,331.0,234.0 background,-59.875,-26.325,47.0,129.0,9.0,1.0,73.0,31.0,43.0,32.0,43.0,10.0,97.0,218.0,339.0,189.0background,-68.375,-15.375,58.0,112.0,10.0,44.0,2039.0,33.0,67.0,31.0,30.0,6.0,101.0,181.0,251.0,133.0 background,-68.525,4.775,72.0,95.0,10.0,0.0,65.0,72.0,16.0,65.0,69.0,133.0,218.0,271.0,346.0,289.0We can run Maxent with “bradypus_swd.csv” as the samples file and “background.csv” (both located in the “swd” directory) as the environmental layers file. Try running it –you’ll notice that it runs much faster, because it doesn’t have to load the big environmental grids. The downside is that it can’t make pictures or output grids, because it doesn’t have all the environmental data. The way to get around this is to use a “projection”, describ ed below.Batch runningSometimes you need to generate a number of models, perhaps with slight variations in the modeling parameters or the inputs. This can be automated using command-line arguments, avoiding the repetition of having to click and type at the program interface. The command line arguments can either be given from a command window (a.k.a. shell), or they can defined in a batch file. Take a look at the file “batchExample.bat” (for example, using Notepad). It contains the following line:java -mx512m -jar maxent.jar environmentallayers=layers togglelayertype=ecoreg samplesfile=samples\bradypus.csv outputdirectory=outputs redoifexists autorunThe effect is to tell the program where to find environmental layers and samples file and where to put outputs, to indicate that the ecoreg variable is categorical. The “autorun” flag tells the program to start running immediately, without waiting for the “Run” button to be pushed. Now try clicking on the file, to see what it does.Many aspects of the Maxent program can be controlled by command-line arguments –press the “Help” button to see all the possibilities. Multiple runs can appear in the same file, and they will simply be run one after the other. You can change the default values of most parameters by adding command-line arguments to the “maxent.bat” file. Regularization.The “regularization multiplier” parameter on the “settings” panel affects how focused the output distribution is – a smaller value will result in a more localized output distribution that fits the given presence records better, but is more prone to overfitting. A larger value will give a more spread-out prediction. Try changing the multiplier, and look at the pictures produced. As an example, setting the multiplier to 3 makes the following picture, showing a much more diffuse distribution than before:ProjectingA model trained on one set of environmental layers can be “projected” by applying it to another set of environmental layers. Situations where projections are needed include modeling species distributions under changing climate conditions, and modeling invasive species. Here we’re going to use projection for a very simple task: making an output grid and associated picture when the samples and background are in SWD format. Type or browse in the samples file entry to point to the file “swd\bradypus_swd.csv”, and similarly for the environmental layers in “swd\background.csv”, then enter the “layers” directory in the “Projection Layers Directory”, as pictur ed below.When you press “Run”, a model is trained on the SWD data, and then projected onto the full grids in the “layers” directory. The output grid is called“bradypus_variegatus_layers.asc”, and in general, the projection directory name is appended to the species name, in order to distinguish it from the standard (un-projected) output. If “make pictures of predictions” is selected, a picture of the projected model will appear in the “bradypus_variegatus.html” file.NOTE: ascii files can be converted into ESRI Grids by using the Ascii to Raster grid command in ArcToolbox.Your assignment is to convert the ascii file into a grid format, display it in ArcMap and create a map layout. Provide an appropriate legend showing the probabilities. Print it out and turn in to class next week.。

研统总结

Unordered categorical variable 等级资料（数据）（ranked data）
有序资料（ordinal data） Ordered categorical variable
categorical variable
定量资料的统计描述
定量资料
集中趋势离散趋势
均数几何均数中位数
完全随机设计：Kruskal-Wallis H test 随机区组设计： Friedman’s M test
两变量（数值）关系的分析(条件）
回归—线性回归（一个自变量、一个应变量）统计描述：回归方程统计推断：b假Yˆ 设a检 b验X (F、t检验)
相关—线性相关（一对一）Pearson’s Corr. Coeff. 统计描述：r 统计推断: r的t检验、查表法
F. Yates & Healy
对生物研究者的忠告：非常痛心地看到，因为数据分析的缺陷和错误，那么好的生物研究工作面临被葬送的危险。
It is a depressing to find how much good biological work is in danger of being wasted through incompetent and misleading of numerical results.
可信区间（CI）：
1、未知，n小 2、未知，n大 3、已知
假设检验
小概率事件（P≤α）
反证法思路（假定H0成立，然后根据样本结果推论是否为小概率事件，如果是则拒绝H0 ，否则不拒绝。）
假设检验是在H0成立的前提下，从样本数据中寻找证据来拒绝H0， “接受”H1；如果证据不足，则不能拒绝H0 , 暂且认为H0正确。

statistical analysis 范文

statistical analysis 范文Statistical analysis is a scientific method that involves collecting, organizing, analyzing, and interpreting data to derive meaningful conclusions and make informed decisions. It is commonly used in various fields such as business, economics, medicine, social sciences, and more. In this article, we will discuss the importance and process of statistical analysis.Statistical analysis plays a crucial role in research as it helps researchers to uncover patterns, relationships, and trends within data. It allows researchers to make inferences about a larger population based on a sample size while minimizing the potential for bias. Statistical analysis also provides a framework for testing hypotheses and making predictions, which is essential for decision-making and problem-solving.The process of statistical analysis starts with clearly defining the research question or problem that needs to be addressed. The researcher then collects relevant data from various sources, ensuring that the sample size is appropriate and representative of the population of interest. The data is then organized and cleaned to eliminate any errors or inconsistencies.Next, the collected data is analyzed using appropriate statistical techniques. Descriptive statistics are used to summarize and describe the data, providing measures such as means, medians, standard deviations, and frequencies. Inferential statistics techniques are then applied to draw conclusions about the population based on the sample data. These techniques include hypothesis testing, confidence intervals, regression analysis, and more.Once the data has been analyzed, the researcher interprets the results and draws meaningful conclusions. This interpretation often involves comparing the results to existing theories or benchmarks and discussing the implications of the findings. The researcher may also identify limitations or areas for further research.In addition to the technical aspects, statistical analysis requires critical thinking and attention to detail. It is essential to select the appropriate statistical techniques based on the research question and data type. Furthermore, it is important to understand the assumptions and limitations of each statistical method and to use them correctly.In conclusion, statistical analysis is a powerful tool that enables researchers to examine and understand data objectively. It provides a systematic approach to analyzing data, drawing conclusions, and making informed decisions. Whether it is in business, healthcare, social sciences, or any other field, statistical analysis is an essential component of research and decision-making processes.。

专八英语阅读

英语专业八级考试TEM-8阅读理解练习册（1）(英语专业2012级)UNIT 1Text AEvery minute of every day, what ecologist生态学家James Carlton calls a global ―conveyor belt‖, redistributes ocean organisms生物.It’s planetwide biological disruption生物的破坏that scientists have barely begun to understand.Dr. Carlton —an oceanographer at Williams College in Williamstown,Mass.—explains that, at any given moment, ―There are several thousand marine species traveling… in the ballast water of ships.‖ These creatures move from coastal waters where they fit into the local web of life to places where some of them could tear that web apart. This is the larger dimension of the infamous无耻的，邪恶的invasion of fish-destroying, pipe-clogging zebra mussels有斑马纹的贻贝.Such voracious贪婪的invaders at least make their presence known. What concerns Carlton and his fellow marine ecologists is the lack of knowledge about the hundreds of alien invaders that quietly enter coastal waters around the world every day. Many of them probably just die out. Some benignly亲切地，仁慈地—or even beneficially — join the local scene. But some will make trouble.In one sense, this is an old story. Organisms have ridden ships for centuries. They have clung to hulls and come along with cargo. What’s new is the scale and speed of the migrations made possible by the massive volume of ship-ballast water压载水— taken in to provide ship stability—continuously moving around the world…Ships load up with ballast water and its inhabitants in coastal waters of one port and dump the ballast in another port that may be thousands of kilometers away. A single load can run to hundreds of gallons. Some larger ships take on as much as 40 million gallons. The creatures that come along tend to be in their larva free-floating stage. When discharged排出in alien waters they can mature into crabs, jellyfish水母, slugs鼻涕虫，蛞蝓, and many other forms.Since the problem involves coastal species, simply banning ballast dumps in coastal waters would, in theory, solve it. Coastal organisms in ballast water that is flushed into midocean would not survive. Such a ban has worked for North American Inland Waterway. But it would be hard to enforce it worldwide. Heating ballast water or straining it should also halt the species spread. But before any such worldwide regulations were imposed, scientists would need a clearer view of what is going on.The continuous shuffling洗牌of marine organisms has changed the biology of the sea on a global scale. It can have devastating effects as in the case of the American comb jellyfish that recently invaded the Black Sea. It has destroyed that sea’s anchovy鳀鱼fishery by eating anchovy eggs. It may soon spread to western and northern European waters.The maritime nations that created the biological ―conveyor belt‖ should support a coordinated international effort to find out what is going on and what should be done about it. (456 words)1.According to Dr. Carlton, ocean organism‟s are_______.A.being moved to new environmentsB.destroying the planetC.succumbing to the zebra musselD.developing alien characteristics2.Oceanographers海洋学家are concerned because_________.A.their knowledge of this phenomenon is limitedB.they believe the oceans are dyingC.they fear an invasion from outer-spaceD.they have identified thousands of alien webs3.According to marine ecologists, transplanted marinespecies____________.A.may upset the ecosystems of coastal watersB.are all compatible with one anotherC.can only survive in their home watersD.sometimes disrupt shipping lanes4.The identified cause of the problem is_______.A.the rapidity with which larvae matureB. a common practice of the shipping industryC. a centuries old speciesD.the world wide movement of ocean currents5.The article suggests that a solution to the problem__________.A.is unlikely to be identifiedB.must precede further researchC.is hypothetically假设地，假想地easyD.will limit global shippingText BNew …Endangered‟ List Targets Many US RiversIt is hard to think of a major natural resource or pollution issue in North America today that does not affect rivers.Farm chemical runoff残渣, industrial waste, urban storm sewers, sewage treatment, mining, logging, grazing放牧,military bases, residential and business development, hydropower水力发电,loss of wetlands. The list goes on.Legislation like the Clean Water Act and Wild and Scenic Rivers Act have provided some protection, but threats continue.The Environmental Protection Agency (EPA) reported yesterday that an assessment of 642,000 miles of rivers and streams showed 34 percent in less than good condition. In a major study of the Clean Water Act, the Natural Resources Defense Council last fall reported that poison runoff impairs损害more than 125,000 miles of rivers.More recently, the NRDC and Izaak Walton League warned that pollution and loss of wetlands—made worse by last year’s flooding—is degrading恶化the Mississippi River ecosystem.On Tuesday, the conservation group保护组织American Rivers issued its annual list of 10 ―endangered‖ and 20 ―threatened‖ rivers in 32 states, the District of Colombia, and Canada.At the top of the list is the Clarks Fork of the Yellowstone River, whereCanadian mining firms plan to build a 74-acre英亩reservoir水库，蓄水池as part of a gold mine less than three miles from Yellowstone National Park. The reservoir would hold the runoff from the sulfuric acid 硫酸used to extract gold from crushed rock.―In the event this tailings pond failed, the impact to th e greater Yellowstone ecosystem would be cataclysmic大变动的，灾难性的and the damage irreversible不可逆转的.‖ Sen. Max Baucus of Montana, chairman of the Environment and Public Works Committee, wrote to Noranda Minerals Inc., an owner of the ― New World Mine‖.Last fall, an EPA official expressed concern about the mine and its potential impact, especially the plastic-lined storage reservoir. ― I am unaware of any studies evaluating how a tailings pond尾矿池，残渣池could be maintained to ensure its structural integrity forev er,‖ said Stephen Hoffman, chief of the EPA’s Mining Waste Section. ―It is my opinion that underwater disposal of tailings at New World may present a potentially significant threat to human health and the environment.‖The results of an environmental-impact statement, now being drafted by the Forest Service and Montana Department of State Lands, could determine the mine’s future…In its recent proposal to reauthorize the Clean Water Act, the Clinton administration noted ―dramatically improved water quality since 1972,‖ when the act was passed. But it also reported that 30 percent of riverscontinue to be degraded, mainly by silt泥沙and nutrients from farm and urban runoff, combined sewer overflows, and municipal sewage城市污水. Bottom sediments沉积物are contaminated污染in more than 1,000 waterways, the administration reported in releasing its proposal in January. Between 60 and 80 percent of riparian corridors (riverbank lands) have been degraded.As with endangered species and their habitats in forests and deserts, the complexity of ecosystems is seen in rivers and the effects of development----beyond the obvious threats of industrial pollution, municipal waste, and in-stream diversions改道to slake消除the thirst of new communities in dry regions like the Southwes t…While there are many political hurdles障碍ahead, reauthorization of the Clean Water Act this year holds promise for US rivers. Rep. Norm Mineta of California, who chairs the House Committee overseeing the bill, calls it ―probably the most important env ironmental legislation this Congress will enact.‖ (553 words)6.According to the passage, the Clean Water Act______.A.has been ineffectiveB.will definitely be renewedC.has never been evaluatedD.was enacted some 30 years ago7.“Endangered” rivers are _________.A.catalogued annuallyB.less polluted than ―threatened rivers‖C.caused by floodingD.adjacent to large cities8.The “cataclysmic” event referred to in paragraph eight would be__________.A. fortuitous偶然的，意外的B. adventitious外加的，偶然的C. catastrophicD. precarious不稳定的，危险的9. The owners of the New World Mine appear to be______.A. ecologically aware of the impact of miningB. determined to construct a safe tailings pondC. indifferent to the concerns voiced by the EPAD. willing to relocate operations10. The passage conveys the impression that_______.A. Canadians are disinterested in natural resourcesB. private and public environmental groups aboundC. river banks are erodingD. the majority of US rivers are in poor conditionText CA classic series of experiments to determine the effects ofoverpopulation on communities of rats was reported in February of 1962 in an article in Scientific American. The experiments were conducted by a psychologist, John B. Calhoun and his associates. In each of these experiments, an equal number of male and female adult rats were placed in an enclosure and given an adequate supply of food, water, and other necessities. The rat populations were allowed to increase. Calhoun knew from experience approximately how many rats could live in the enclosures without experiencing stress due to overcrowding. He allowed the population to increase to approximately twice this number. Then he stabilized the population by removing offspring that were not dependent on their mothers. He and his associates then carefully observed and recorded behavior in these overpopulated communities. At the end of their experiments, Calhoun and his associates were able to conclude that overcrowding causes a breakdown in the normal social relationships among rats, a kind of social disease. The rats in the experiments did not follow the same patterns of behavior as rats would in a community without overcrowding.The females in the rat population were the most seriously affected by the high population density: They showed deviant异常的maternal behavior; they did not behave as mother rats normally do. In fact, many of the pups幼兽，幼崽, as rat babies are called, died as a result of poor maternal care. For example, mothers sometimes abandoned their pups,and, without their mothers' care, the pups died. Under normal conditions, a mother rat would not leave her pups alone to die. However, the experiments verified that in overpopulated communities, mother rats do not behave normally. Their behavior may be considered pathologically 病理上，病理学地diseased.The dominant males in the rat population were the least affected by overpopulation. Each of these strong males claimed an area of the enclosure as his own. Therefore, these individuals did not experience the overcrowding in the same way as the other rats did. The fact that the dominant males had adequate space in which to live may explain why they were not as seriously affected by overpopulation as the other rats. However, dominant males did behave pathologically at times. Their antisocial behavior consisted of attacks on weaker male,female, and immature rats. This deviant behavior showed that even though the dominant males had enough living space, they too were affected by the general overcrowding in the enclosure.Non-dominant males in the experimental rat communities also exhibited deviant social behavior. Some withdrew completely; they moved very little and ate and drank at times when the other rats were sleeping in order to avoid contact with them. Other non-dominant males were hyperactive; they were much more active than is normal, chasing other rats and fighting each other. This segment of the rat population, likeall the other parts, was affected by the overpopulation.The behavior of the non-dominant males and of the other components of the rat population has parallels in human behavior. People in densely populated areas exhibit deviant behavior similar to that of the rats in Calhoun's experiments. In large urban areas such as New York City, London, Mexican City, and Cairo, there are abandoned children. There are cruel, powerful individuals, both men and women. There are also people who withdraw and people who become hyperactive. The quantity of other forms of social pathology such as murder, rape, and robbery also frequently occur in densely populated human communities. Is the principal cause of these disorders overpopulation? Calhoun’s experiments suggest that it might be. In any case, social scientists and city planners have been influenced by the results of this series of experiments.11. Paragraph l is organized according to__________.A. reasonsB. descriptionC. examplesD. definition12．Calhoun stabilized the rat population_________.A. when it was double the number that could live in the enclosure without stressB. by removing young ratsC. at a constant number of adult rats in the enclosureD. all of the above are correct13.W hich of the following inferences CANNOT be made from theinformation inPara. 1?A. Calhoun's experiment is still considered important today.B. Overpopulation causes pathological behavior in rat populations.C. Stress does not occur in rat communities unless there is overcrowding.D. Calhoun had experimented with rats before.14. Which of the following behavior didn‟t happen in this experiment?A. All the male rats exhibited pathological behavior.B. Mother rats abandoned their pups.C. Female rats showed deviant maternal behavior.D. Mother rats left their rat babies alone.15. The main idea of the paragraph three is that __________.A. dominant males had adequate living spaceB. dominant males were not as seriously affected by overcrowding as the otherratsC. dominant males attacked weaker ratsD. the strongest males are always able to adapt to bad conditionsText DThe first mention of slavery in the statutes法令，法规of the English colonies of North America does not occur until after 1660—some forty years after the importation of the first Black people. Lest we think that existed in fact before it did in law, Oscar and Mary Handlin assure us, that the status of B lack people down to the 1660’s was that of servants. A critique批判of the Handlins’ interpretation of why legal slavery did not appear until the 1660’s suggests that assumptions about the relation between slavery and racial prejudice should be reexamined, and that explanation for the different treatment of Black slaves in North and South America should be expanded.The Handlins explain the appearance of legal slavery by arguing that, during the 1660’s, the position of white servants was improving relative to that of black servants. Thus, the Handlins contend, Black and White servants, heretofore treated alike, each attained a different status. There are, however, important objections to this argument. First, the Handlins cannot adequately demonstrate that t he White servant’s position was improving, during and after the 1660’s; several acts of the Maryland and Virginia legislatures indicate otherwise. Another flaw in the Handlins’ interpretation is their assumption that prior to the establishment of legal slavery there was no discrimination against Black people. It is true that before the 1660’s Black people were rarely called slaves. But this shouldnot overshadow evidence from the 1630’s on that points to racial discrimination without using the term slavery. Such discrimination sometimes stopped short of lifetime servitude or inherited status—the two attributes of true slavery—yet in other cases it included both. The Handlins’ argument excludes the real possibility that Black people in the English colonies were never treated as the equals of White people.The possibility has important ramifications后果，影响.If from the outset Black people were discriminated against, then legal slavery should be viewed as a reflection and an extension of racial prejudice rather than, as many historians including the Handlins have argued, the cause of prejudice. In addition, the existence of discrimination before the advent of legal slavery offers a further explanation for the harsher treatment of Black slaves in North than in South America. Freyre and Tannenbaum have rightly argued that the lack of certain traditions in North America—such as a Roman conception of slavery and a Roman Catholic emphasis on equality— explains why the treatment of Black slaves was more severe there than in the Spanish and Portuguese colonies of South America. But this cannot be the whole explanation since it is merely negative, based only on a lack of something. A more compelling令人信服的explanation is that the early and sometimes extreme racial discrimination in the English colonies helped determine the particular nature of the slavery that followed. (462 words)16. Which of the following is the most logical inference to be drawn from the passage about the effects of “several acts of the Maryland and Virginia legislatures” (Para.2) passed during and after the 1660‟s?A. The acts negatively affected the pre-1660’s position of Black as wellas of White servants.B. The acts had the effect of impairing rather than improving theposition of White servants relative to what it had been before the 1660’s.C. The acts had a different effect on the position of white servants thandid many of the acts passed during this time by the legislatures of other colonies.D. The acts, at the very least, caused the position of White servants toremain no better than it had been before the 1660’s.17. With which of the following statements regarding the status ofBlack people in the English colonies of North America before the 1660‟s would the author be LEAST likely to agree?A. Although black people were not legally considered to be slaves,they were often called slaves.B. Although subject to some discrimination, black people had a higherlegal status than they did after the 1660’s.C. Although sometimes subject to lifetime servitude, black peoplewere not legally considered to be slaves.D. Although often not treated the same as White people, black people,like many white people, possessed the legal status of servants.18. According to the passage, the Handlins have argued which of thefollowing about the relationship between racial prejudice and the institution of legal slavery in the English colonies of North America?A. Racial prejudice and the institution of slavery arose simultaneously.B. Racial prejudice most often the form of the imposition of inheritedstatus, one of the attributes of slavery.C. The source of racial prejudice was the institution of slavery.D. Because of the influence of the Roman Catholic Church, racialprejudice sometimes did not result in slavery.19. The passage suggests that the existence of a Roman conception ofslavery in Spanish and Portuguese colonies had the effect of _________.A. extending rather than causing racial prejudice in these coloniesB. hastening the legalization of slavery in these colonies.C. mitigating some of the conditions of slavery for black people in these coloniesD. delaying the introduction of slavery into the English colonies20. The author considers the explanation put forward by Freyre andTannenbaum for the treatment accorded B lack slaves in the English colonies of North America to be _____________.A. ambitious but misguidedB. valid有根据的but limitedC. popular but suspectD. anachronistic过时的，时代错误的and controversialUNIT 2Text AThe sea lay like an unbroken mirror all around the pine-girt, lonely shores of Orr’s Island. Tall, kingly spruce s wore their regal王室的crowns of cones high in air, sparkling with diamonds of clear exuded gum流出的树胶; vast old hemlocks铁杉of primeval原始的growth stood darkling in their forest shadows, their branches hung with long hoary moss久远的青苔;while feathery larches羽毛般的落叶松,turned to brilliant gold by autumn frosts, lighted up the darker shadows of the evergreens. It was one of those hazy朦胧的, calm, dissolving days of Indian summer, when everything is so quiet that the fainest kiss of the wave on the beach can be heard, and white clouds seem to faint into the blue of the sky, and soft swathing一长条bands of violet vapor make all earth look dreamy, and give to the sharp, clear-cut outlines of the northern landscape all those mysteries of light and shade which impart such tenderness to Italian scenery.The funeral was over,--- the tread鞋底的花纹/ 踏of many feet, bearing the heavy burden of two broken lives, had been to the lonely graveyard, and had come back again,--- each footstep lighter and more unconstrained不受拘束的as each one went his way from the great old tragedy of Death to the common cheerful of Life.The solemn black clock stood swaying with its eternal ―tick-tock, tick-tock,‖ in the kitchen of the brown house on Orr’s Island. There was there that sense of a stillness that can be felt,---such as settles down on a dwelling住处when any of its inmates have passed through its doors for the last time, to go whence they shall not return. The best room was shut up and darkened, with only so much light as could fall through a little heart-shaped hole in the window-shutter,---for except on solemn visits, or prayer-meetings or weddings, or funerals, that room formed no part of the daily family scenery.The kitchen was clean and ample, hearth灶台, and oven on one side, and rows of old-fashioned splint-bottomed chairs against the wall. A table scoured to snowy whiteness, and a little work-stand whereon lay the Bible, the Missionary Herald, and the Weekly Christian Mirror, before named, formed the principal furniture. One feature, however, must not be forgotten, ---a great sea-chest水手用的储物箱,which had been the companion of Zephaniah through all the countries of the earth. Old, and battered破旧的，磨损的, and unsightly难看的it looked, yet report said that there was good store within which men for the most part respect more than anything else; and, indeed it proved often when a deed of grace was to be done--- when a woman was suddenly made a widow in a coast gale大风，狂风, or a fishing-smack小渔船was run down in the fogs off the banks, leaving in some neighboring cottage a family of orphans,---in all such cases, the opening of this sea-chest was an event of good omen 预兆to the bereaved丧亲者;for Zephaniah had a large heart and a large hand, and was apt有…的倾向to take it out full of silver dollars when once it went in. So the ark of the covenant约柜could not have been looked on with more reverence崇敬than the neighbours usually showed to Captain Pennel’s sea-chest.1. The author describes Orr‟s Island in a(n)______way.A.emotionally appealing, imaginativeB.rational, logically preciseC.factually detailed, objectiveD.vague, uncertain2.According to the passage, the “best room”_____.A.has its many windows boarded upB.has had the furniture removedC.is used only on formal and ceremonious occasionsD.is the busiest room in the house3.From the description of the kitchen we can infer that thehouse belongs to people who_____.A.never have guestsB.like modern appliancesC.are probably religiousD.dislike housework4.The passage implies that_______.A.few people attended the funeralB.fishing is a secure vocationC.the island is densely populatedD.the house belonged to the deceased5.From the description of Zephaniah we can see thathe_________.A.was physically a very big manB.preferred the lonely life of a sailorC.always stayed at homeD.was frugal and saved a lotText BBasic to any understanding of Canada in the 20 years after the Second World War is the country' s impressive population growth. For every three Canadians in 1945, there were over five in 1966. In September 1966 Canada's population passed the 20 million mark. Most of this surging growth came from natural increase. The depression of the 1930s and the war had held back marriages, and the catching-up process began after 1945. The baby boom continued through the decade of the 1950s, producing a population increase of nearly fifteen percent in the five years from 1951 to 1956. This rate of increase had been exceeded only once before in Canada's history, in the decade before 1911 when the prairies were being settled. Undoubtedly, the good economic conditions of the 1950s supported a growth in the population, but the expansion also derived from a trend toward earlier marriages and an increase in the average size of families; In 1957 the Canadian birth rate stood at 28 per thousand, one of the highest in the world. After the peak year of 1957, thebirth rate in Canada began to decline. It continued falling until in 1966 it stood at the lowest level in 25 years. Partly this decline reflected the low level of births during the depression and the war, but it was also caused by changes in Canadian society. Young people were staying at school longer, more women were working; young married couples were buying automobiles or houses before starting families; rising living standards were cutting down the size of families. It appeared that Canada was once more falling in step with the trend toward smaller families that had occurred all through theWestern world since the time of the Industrial Revolution. Although the growth in Canada’s population had slowed down by 1966 (the cent), another increase in the first half of the 1960s was only nine percent), another large population wave was coming over the horizon. It would be composed of the children of the children who were born during the period of the high birth rate prior to 1957.6. What does the passage mainly discuss?A. Educational changes in Canadian society.B. Canada during the Second World War.C. Population trends in postwar Canada.D. Standards of living in Canada.7. According to the passage, when did Canada's baby boom begin?A. In the decade after 1911.B. After 1945.C. During the depression of the 1930s.D. In 1966.8. The author suggests that in Canada during the 1950s____________.A. the urban population decreased rapidlyB. fewer people marriedC. economic conditions were poorD. the birth rate was very high9. When was the birth rate in Canada at its lowest postwar level?A. 1966.B. 1957.C. 1956.D. 1951.10. The author mentions all of the following as causes of declines inpopulation growth after 1957 EXCEPT_________________.A. people being better educatedB. people getting married earlierC. better standards of livingD. couples buying houses11.I t can be inferred from the passage that before the IndustrialRevolution_______________.A. families were largerB. population statistics were unreliableC. the population grew steadilyD. economic conditions were badText CI was just a boy when my father brought me to Harlem for the first time, almost 50 years ago. We stayed at the hotel Theresa, a grand brick structure at 125th Street and Seventh avenue. Once, in the hotel restaurant, my father pointed out Joe Louis. He even got Mr. Brown, the hotel manager, to introduce me to him, a bit punchy强力的but still champ焦急as fast as I was concerned.Much has changed since then. Business and real estate are booming. Some say a new renaissance is under way. Others decry责难what they see as outside forces running roughshod肆意践踏over the old Harlem. New York meant Harlem to me, and as a young man I visited it whenever I could. But many of my old haunts are gone. The Theresa shut down in 1966. National chains that once ignored Harlem now anticipate yuppie money and want pieces of this prime Manhattan real estate. So here I am on a hot August afternoon, sitting in a Starbucks that two years ago opened a block away from the Theresa, snatching抓取，攫取at memories between sips of high-priced coffee. I am about to open up a piece of the old Harlem---the New York Amsterdam News---when a tourist。

计量经济学stata英文论文

Graduates to apply for the quantitative analysis of changes in number of graduatestudents一Topics raisedIn this paper, the total number of students from graduate students (variable) multivariate analysis (see below) specific analysis, and collect relevant data, model building, this quantitative analysis. The number of relations between the school the total number of graduate students with the major factors, according to the size of the various factors in the coefficient in the model equations, analyze the importance of various factors, exactly what factors in changes in the number of graduate students aspects play a key role in and changes in the trend for future graduate students to our proposal.The main factors affect changes in the total number of graduate students for students are as follows：Per capita GDP - which is affecting an important factor to the total number of students in the graduate students (graduate school is not a small cost, and only have a certain economic base have more opportunities for post-graduate)The total population - it will affect the total number of students in graduate students is an important factor (it can be said to affect it is based on source)The number of unemployed persons - this is the impact of adirect factor of the total number of students in the graduatestudents (it is precisely because of the high unemployment rate,will more people choose Kaoyan will be their own employment weights)Number of colleges and universities - which is to influenceprecisely because of the emergence of more institutions of higherlearning in the school the total number of graduate students is nota small factor (to allow more people to participate in Kaoyan)二 Establish ModelY=α+β1X1+β2X2+β3X3+β4X4 +uAmong them, theY-in the total number of graduate students (variable)X1 - per capita GDP (explanatory variables)X2 - the total population (explanatory variables)X3 - the number of unemployed persons (explanatory variables)X4 - the number of colleges and universities (explanatory variables)三、Data collection1.date ExplainHere, using the same area (ie, China) time-series data were fitted2.Data collectionTime series data from 1986 to 2005, the specific circumstances are shown in Table 1Table 1：Y X1X2X3X41986110371963107507264.4105419871201911112109300276.6106319881127761366111026296.2107519891013391519112704377.910751990930181644114333383.210751991881281893115823352.210751992941642311117171363.9105319931067712998118517420.1106519941279354044119850476.4108019951454435046121121519.6105419961633225846122389552.8103219971763536420123626576.81020199819888567961247615711022199923351371591257865751071200030123978581267435951041200139325686221276276811225200250098093981284537701396200365126010542129227800155220048198961233612998882717312005978610140401307568391792四、Model parameter estimation, inspection and correction1.Model parameter estimation and its economic significance, statistical inference test. twoway(scatter Y X1)2000004000006000008000001.0e +06twoway(scatter Y X2)2000004000006000008000001.0e +06twoway(scatter Y X3)2000004000006000008000001.0e +06twoway(scatter Y X4)2000004000006000008000001.0e +0graph twoway lfit y X1200000400000600000800000F i t t e d v a l u e sgraph twoway lfit y X2-20000020000040000060000F i t t e d v a l u e sgraph twoway lfit y X3200000400000600000800000F i t t e d v a l u e sgraph twoway lfit y X42000004000006000008000001000000F i t t e d v a l u e s_cons 270775.2 369252.9 0.73 0.475 -516268.7 1057819 X4 621.3348 46.72257 13.30 0.000 521.748 720.9216 X3 -366.8774 157.9402 -2.32 0.035 -703.5189 -30.23585 X2 -7.158603 3.257541 -2.20 0.044 -14.10189 -.2153182 X1 59.22455 6.352288 9.32 0.000 45.68496 72.76413 Y Coef. Std. Err. t P>|t| [95% Conf. Interval] Total 1.3040e+12 19 6.8631e+10 Root MSE = 18535 Adj R-squared = 0.9950 Residual 5.1533e+09 15 343556320 R-squared = 0.9960 Model 1.2988e+12 4 3.2471e+11 Prob > F = 0.0000 F( 4, 15) = 945.14 Source SS df MS Number of obs = 20. reg Y X1 X2 X3 X4Y = 59.22454816*X1- 7.158602346*X2- 366.8774279*X3+621.3347694*X4（6.352288）（3.257541）（157.9402）（46.72256）t= （9.323341）（-2.197548）（-2.322889）（13.29839）+ 270775.151（369252.8）（0.733306）R2=0.996048 Adjusted R-squared=0.994994 F=945.1415DW=1.596173Visible, X1, X2, X3, X4 t values are significant, indicating that the per capita GDP, the total population of registered urban unemployed population, the number of colleges and universities are the main factors affecting the total number of graduate students in school. Model coefficient of determination for 0.996048 amendments coefficient of determination of 0.994994, was relatively large, indicating high degree of model fit, while the F value of 945.1415, indicating that the model overall is significant。

计量经济学英文解释

计量经济学英文解释English:Econometrics is a branch of economics that applies statistical methods and mathematical models to analyze and quantify the relationships between economic variables. It aims to provide empirical evidence and test economic theories by using real-world data. By employing various econometric techniques, such as regression analysis, time series analysis, and panel data analysis, econometricians are able to estimate and measure the parameters of economic models, assess the significance of different factors, and make predictions or forecasts about future economic outcomes. Econometrics plays a crucial role in several areas of economics, including macroeconomics, microeconomics, finance, and labor economics, as it helps in understanding economic phenomena, formulating economic policies, and making informed decisions. In addition to its theoretical applications, econometrics also has practical applications in business, government, and research institutions where data-driven decision-making is important. Overall, econometrics provides a systematic and quantitative approach toeconomics, allowing economists to study and analyze economic behavior and relationships in a rigorous and scientific manner.中文翻译:计量经济学是经济学的一个分支，它应用统计方法和数学模型来分析和量化经济变量之间的关系。

statistical 例句

statistical 例句1. The statistical analysis of the data revealed significant differences between the two groups.2. According to the statistical report, the average income in the country has increased by 10%.3. Statistical methods were used to analyze the relationship between variables in the study.4. The statistical software allows for easy manipulation and visualization of complex data sets.5. The statistical significance of the results was confirmed through hypothesis testing.6. The study relied on a large sample size to ensure statistical power.7. Statistical outliers were identified and removed from the data set.8. The statistical distribution of the data was found to be skewed to the right.9. The statistical model accurately predicted the outcome of the experiment.10. The statistical analysis uncovered a correlation between two previously unrelated variables.11. Statistical techniques were used to control for confounding variables in the study.12. The statistical software provided descriptive statistics for the data set.13. The statistical inference drawn from the sample was applied to the population at large.14. The statistical evidence supported the conclusionthat there is a relationship between the two variables.15. Statistical programming languages allow for the automation of data analysis processes.16. The statistical method used was deemed appropriate for the research question.17. The statistical consultant provided expertise on the best methods for analyzing the data.18. Statistical tests were conducted to determine the significance of the findings.19. The statistical analysis revealed a clear trend in the data over time.20. The statistical model accurately represented the underlying patterns in the data.21. Statistical measures such as mean, median, and mode were used to summarize the data.22. The statistical significance of the results was confirmed through a p-value of less than 0.05.23. The statistical software provided graphical representations of the data for better understanding.24. The statistical approach to the problem proved to be effective in identifying patterns in the data.25. Statistical quality control methods were used to monitor production processes in the factory.26. The statistical distribution of the data set was found to be normal.27. Statistical techniques such as regression analysis were employed to understand the relationships between variables.28. The statistical findings were presented in a clear and accessible manner for easy interpretation.29. The statistical trends in the data were analyzed to inform future decision-making.30. Statistical tools such as ANOVA were used to compare means between multiple groups.31. The statistical analysis confirmed the hypothesisthat there was a significant difference between the two conditions.32. The statistical approach allowed for theidentification of patterns in the data that were previously overlooked.33. Statistical process control was implemented to monitor and improve the quality of the manufacturing process.34. The statistical analysis revealed no significant difference between the two groups, contrary to the initial hypothesis.35. The statistical software allowed for thevisualization of the data through various types of charts and graphs.36. The statistical modeling of the data allowed for the prediction of future trends.37. Statistical techniques such as chi-square tests were used to analyze categorical data.38. The statistical evidence supported the conclusionthat the intervention had a significant impact on the outcome.39. A statistical analysis plan was developed to outline the methods for analyzing the data.40. The statistical approach to the problem allowed for a deeper understanding of the underlying factors at play.41. Statistical significance was determined using a confidence interval of 95%.42. The statistical findings were cross-validated with an independent data set to ensure their reliability.43. The statistical analysis provided valuable insights into the behavior of the variables in the study.44. Statistical techniques such as cluster analysis were used to group similar data points together.45. The statistical software provided a wide range of tools for exploratory data analysis.46. The statistical model accurately predicted the outcome of the experiment with a high degree of confidence.47. Statistical outliers were identified and further investigated to understand their impact on the results.48. The statistical report highlighted key findings and their implications for future research.49. The statistical inference drawn from the sample was extrapolated to the larger population.50. The statistical software allowed for the calculation of basic descriptive statistics for the data set.51. Statistical tests of significance were conducted to determine the reliability of the results.。

最大熵原理及其在生态学研究中的应用(1)

摘要: 最大熵原理(the principle of maximum entropy)起源于信息论和统计力学, 是基于有限的已知信息对未知分布进行无偏推断的一种数学方法。这一方法在很多领域都有成功应用, 但只是近几年才被应用到生态学研究中, 并且还存在很多争论。我们从基本概念和方法出发, 用掷骰子的例子阐明了最大熵原理的概念, 并提出运用最大熵原理解决问题需要遵从的步骤。最大熵原理在生态学中的应用主要包括以下方面: (1)用群落水平功能性状的平均值作为约束条件来预测群落物种相对多度的模型; (2)基于气候、海拔、植被等环境因子构建物种地理分布的生态位模型; (3)对物种多度分布、种–面积关系等宏生态学格局的推断; (4)对物种相互作用的推断; (5)对食物网度分布的研究等等。最后我们综合分析了最大熵原理在生态学应用中所存在的争议, 包括相应模型的有效性、可靠性等方面, 介绍了一些对最大熵原理预测能力及其局限性的检验结果, 强调了生态学家应用最大熵原理需要注意的问题, 比如先验分布的选择、约束条件的设置等等。在物种相互作用、宏生态学格局等方面对最大熵原理更广泛的讨论与应用可能会给生态学带来新的发展机会。关键词: 最大熵方法, 贝叶斯统计, 植物性状, 物种地理分布, 宏生态学, 物种相互作用, 度分布, 中性理论
Abstract: The principle of maximum entropy (MaxEnt) was originally studied in information theory and statistical mechanics, and was widely employed in a variety of contexts. MaxEnt provides a statistical inference of unknown distributions on the basis of partial knowledge without taking into any unknown information. Recently there has been growing interest in the use of MaxEnt in ecology. In this review, to provide an intuitive understanding of this principle, we firstly employ an example of dice throwing to demonstrate the underlying basis of MaxEnt, and list the steps one should take when applying this principle. Then we focus on its applications in some fields of ecology and biodiversity, including the predicting of species relative abundances using community aggregated traits (CATs), the MaxEnt niche model of biogeography based on environmental factors, the studying of macroecology patterns such as species abundance distribution (SAD) and species–area relationship (SAR), inferences of species interactions using species abundance matrix or merely occurrence (presence/absence) data, and the predicting of food web degree distributions. We also highlight the main debates about these applications and some recent tests of these models' strengths and limitations. We conclude with the discussion of some matters of attention ecologists should keep in mind when using MaxEnt. Key words: MaxEnt, Bayesian statistics, plant traits, species geographic distribution, macroecology, species interactions, degree distributions, neutral theory

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altitude values where the species was observed
MaxEnt optimizes two conﬂicting criteria:
• p(Altitude | observed) should be high for the
• Maximize the log-likelihood
Presence-only modeling
P(observation | environment) P(environment | observation) P(environment)
Elith et al. 2010
Sites with Blue Jays Frequency
Sites in general Altitude
X X X X X X X X X X X XX X X
Google Maps
Presence-only modeling
Presence-only modeling
No idea:
• Where sampling took place • How many samples were taken
different from p(Altitude)
• Minimize the absolute value of the parameters
MaxEnt optimizes two conﬂicting criteria:
• p(Altitude | observed) should be high for the
Proportional to exp(ax + bx2 + cxy ....)
Elith et al. 2010
Interpreting the outputs
Interpreting the outputs
• Raw output: proportional to
p(present | environment)
A statistical explanation of MaxEnt for ecologists
Presentation by David J. Harris paper by Jane Elith et al. 2010
Altitude data from Worldclim Blue Jay occurrence data from Breeding Bird Survey
Presence-only modeling
No idea:
• Where sampling took place • How many samples were taken
Need to assume samples came independently from a known distribution
Altitude
1) Deﬁne the model so this null hypothesis, p(Altitude | observed) = p(Altitude), is where all parameters = 0
1) Deﬁne the model so this null hypothesis, p(Altitude | observed) = p(Altitude), is where all parameters = 0
Presence-only modeling
Presence-only modeling
P(observation | environment)
Presence-only modeling
P(observation | environment)
Presence-only modeling
P(observation | environment) P(environment | observation)
Maxent
• Widely used • Good performance • Point-and-click workﬂow • Totally foreign jargon/notation/approach • Elith et al. 2010 to the rescue!
Maxent without all that “entropy” stuff
Sites in general Altitude
p(Altitude | observed) p(Altitude)
Ratio of kernel density estimators
GAM

Sites with Blue Jays
Frequency
Sites in general Altitude
• p(Altitude | observed) should be high for the
• Maximize the log-likelihood
altitude values where the species was observed
• p(Altitude | observed) shouldn’t be too
altitude values where the species was observed
• p(Altitude | observed) shouldn’t be too
different from p(Altitude)
MaxEnt optimizes two conﬂicting criteria:
Gibbs distributions
• • Linear stuff in the exponent controls mean • Squared stuff in the exponent controls variance
Proportional to exp(ax + bx2 + cxy ....)
“Features”
Model output
Transformed environmental variables
Measured environmental variables
Model output
Transformed environmental variables
Trees, splines, polynomials, etc.
Gibbs distributions
• • Linear stuff in the exponent controls mean • Squared stuff in the exponent controls variance • Products in the exponent control covariance
• Maximize the log-likelihood
altitude values where the species was observed
• p(Altitude | observed) shouldn’t be too
different from p(Altitude)
• Minimize the absolute value of the parameters • In Bayesian terms, this is a Laplace prior
Maxent
Maxent
• Widely used
Maxent
• Widely used • Good performance
Maxent
• Widely used • Good performance • Point-and-click workﬂow
Maxent
• Widely used • Good performance • Point-and-click workﬂow • Totally foreign jargon/notation/approach
Proportional to exp(ax + bx2 + cxy ....)
Gibbs distributions
• • Linear stuff in the exponent controls mean • Squared stuff in the exponent controls variance • Products in the exponent control covariance • Other stuff can make fancier shapes
Sites with Blue Jays Frequency
p(Altitude | observed) p(Altitude)
Sites in general Altitude
Sites with Blue Jays Frequency
p(observed | Altitude)
∝
p(Altitude | observed) p(Altitude)
How would we estimate it if we had no occurrence data?
Sites in general Altitude
Frequency
Sites with Blue Jays Frequency
Key insight behind MaxEnt!
Sites in general Altitude
• Widely used • Good performance • Point-and-click workﬂow • Totally foreign jargon/notation/approach • Elith et al. 2010 to the rescue!
Presence-absence modeling
Sites with Blue Jays