Importance Sampling and the Method of Simulated Moments

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贝叶斯统计-教学大纲

《贝叶斯统计》教学大纲“Bayesian Statistics” Course Outline课程编号：152053A课程类型：专业选修课总学时：48 讲课学时：48实验（上机）学时：0学分：3适用对象：金融学（金融经济）先修课程：数学分析、概率论与数理统计、计量经济学Course Code：152053ACourse Type：Discipline ElectiveTotal Hours：48 Lecture：48Experiment(Computer)：0Credit：3Applicable Major：Finance（Finance and Economics Experiment Class）Prerequisite：Mathematical Analysis, Probability Theory and Statistics, Econometrics一、课程的教学目标本课程旨在向学生介绍贝叶斯统计理论、贝叶斯统计方法及其在实证研究中的应用。

贝叶斯统计理论与传统统计理论遵循着不同的基本假设，为我们处理数据信息提供新的角度和解读思路，并在处理某些复杂模型上（如，估计动态随机一般均衡模型、带时变参数的状态空间模型等）相比传统方法具有相对优势。

本课程要求学生在选课前具备基本的微积分、概率统计以及计量经济学知识。

以此为起点，我们将主要就贝叶斯统计理论知识、统计模型的应用以及基于计算机编程的实证能力三方面对学生进行训练。

经过对本课程的学习，学生应了解贝叶斯框架的基本思想，掌握基本的贝叶斯理论方法及其主要应用，并掌握实证研究中常用的贝叶斯数值抽样方法以及相关的计算机编程技能。

特别地，学生应能明确了解贝叶斯统计方法与传统统计方法在思想和应用上的区别以及各自的优缺点，以便能在实际应用中合理选择统计分析工具。

This course introduces the basic concepts of Bayesian statistics and the use of Bayesian econometric methods in empirical study. Bayesian statistics has different fundamental assumptions from the classical (frequentist) framework, providing us with an alternative way in analyzing and interpreting data information. Bayesian methods also have relative advantages, and thus are widely used, in dealing with certain complicated models (for example, the estimation of Dynamic Stochastic General Equilibrium model, state space models with time-varying parameters, etc.).Students should have had basic trainings on calculus, probability theory and statistics, and preferably econometrics prior to this course. The major trainings offered in this course focus on Bayesian theories, Bayesian statistical models with applications and computational skills required for empirical analysis. After the course, students should develop their understanding on the philosophy of Bayesian framework, understand basic Bayesian theories, Bayesian estimation methods and their applications, and master the computer skills for the practical use of Bayesian methods. Specifically, students should understand the differences between the Bayesian viewpoint and the classical frequentist perspective in order to be able to choose appropriate analyzing tools in empirical use.二、教学基本要求贝叶斯统计学和计量方法在近年得到越来越广泛的关注和应用，主要得益于计算机技术的发展使得贝叶斯数值抽样方法在实际应用中得以实现。

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.。

evidence based method

Evidence-Based Method随着科学技术的不断进步，我们面临的问题和挑战也日益复杂多样。

在这种情况下，依靠科学的证据来解决问题成为了一种十分重要的方法。

Evidence-based method，即基于证据的方法，指的是通过收集、分析和运用科学证据来做出决策和解决问题的一种方法。

在医学、教育、管理、政策制定等领域，Evidence-based method都得到了广泛的应用和推崇。

本文将从以下几个方面来探讨Evidence-based method的意义、特点及应用。

1. 证据的重要性在决策和问题解决过程中，经验和直觉固然重要，但更加可靠和稳健的方法是依据科学的证据来做出决策。

因为证据是客观的、可量化的，能够帮助我们避免主观偏见和错误的判断。

在医疗领域，医生通常会根据临床试验的结果以及大量的研究数据来选择最佳的治疗方案，而不是仅仅依据自己的经验和直觉。

在教育领域，教育工作者也应该依据教育心理学和教育研究的成果来设计课程和教学方法，以提高教学效果。

证据的重要性无论在个人生活还是专业领域都是不可忽视的。

2. Evidence-based method的特点Evidence-based method与传统的经验主义方法有着明显的不同点。

Evidence-based method强调的是基于大量的科学研究和实证数据，而不是基于个人或小范围的经验。

Evidence-based method更加注重系统性和客观性，它需要进行严格的数据收集、分析和评估，以确保所得出的结论是客观和可靠的。

Evidence-based method还要求对证据进行合理的解释和运用，避免片面地使用证据来支持某种观点或立场。

3. Evidence-based method的应用在各个领域，Evidence-based method都有着广泛的应用。

在医学领域，Evidence-based medicine已经成为了临床实践的重要方法之一，它不仅能够帮助医生选择最佳的治疗方案，还能够提高医疗机构的管理效率和医疗资源的利用率。

管理学期末复习(中英文汇总)

第一章1.1管理者对组织很重要原因（1）在这个复杂、混乱和不确定的时代，组织需要他们的管理技能和能力（2）管理者对工作的顺利完成至关重要（3）有助于提高员工的生产率和忠诚度（4）对创造组织价值观很重要1.2管理者协调和监督其他人工作，以实现组织目标。

在传统结构的组织中，管理者可以被划分为基层、中层和高层管理者。

组织的三个特征：一个明确的目标；由人员组成；一种精细的结构1.3 广义上，管理就是管理者所从事的工作。

管理者协调和监管其他人以有效率、有效果的方式完成他们的工作或任务。

效率是以正确的方式做事；效果是做正确的事管理的四种只能：计划（定义目标、制定战略、制定计划）；组织（对工作作出安排）；领导（与其他人共事并且通过他们完成目标）；控制（对工作绩效进行监控、比较或纠正）明茨伯格的管理角色(Mintzberg’s managerial roles)包括（1）人际关系角色（Interpersonal):挂名首脑figurehead领导者leader联络者liaison，这涉及与人打交道以及其他仪式性/象征性ceremonial/symbolic的活动（2）信息传递角色informational:监听者monitor传播者dissemination发言人spokesperson，指的是收集collecting、接受receiving和传播disseminating信息；（3）决策定制者decisional：企业家entrepreneur、混乱驾驭者disturbance handler、资源配置者resource allocator和谈判者negotiator，即制定决策管理者以三种方式来影响行为：通过对行为进行直接管理；通过对采取行动的人员进行管理；通过对推动人们采取行动的信息进行管理managing information that impels people to take action。

卡茨认为，管理技能包括katz’s managerial skills：技术技能technical（与具体工作相关的知识和技术）、人际技能human skill（与他人和谐共事的能力）和概念能力conceptual（思考和表达创意的能力）。

Greedy importance sampling

type results in a high variance estimator since the sample will almost always contains un-
representative points but will intermittently be dominatБайду номын сангаасd by a few high weight points. The
ing for important regions in the target distribution È . Previous work has shown that search
can be incorporated in an importance sampler while maintaining unbiasedness, leading to improved estimation in simple problems. However, the drawbacks of the previous GIS method are that it has free parameters whose settings affect estimation performance, and its importance weights are directed at achieving unbiasedness without necessarily being directed at reducing variance. In this paper, we introduce a new, parameterless form of greedy importance sampling that performs comparably to the previous method given its best parameter settings. We then introduce a new weight calculation scheme that preserves unbiasedness, but provides further variance reduction by “regularizing” the contributions each search path gives to the estimator. We ﬁnd that the new procedure signiﬁcantly improves the original technique and achieves competitive results on difﬁcult estimation problems arising in large discrete domains, such as those posed by Boltzmann machines. Below we ﬁrst review the generalized importance sampling procedure that forms the core of our estimators before describing the innovations that lead to improved estimators.

利用重要性采样提高深度学习模型的学习效率

利用重要性采样提高深度学习模型的学习效率深度学习在计算机科学和人工智能领域中取得了巨大的成功。

然而，深度学习模型的训练往往需要大量的时间和计算资源，尤其是当处理大规模数据集时，会面临训练过程变慢的问题。

重要性采样（importance sampling）是一种常用的方法，可用于提高深度学习模型的学习效率。

本文将探讨重要性采样的原理和在深度学习中的应用。

重要性采样是一种用于减少采样偏差并提高采样效率的技术。

在深度学习中，模型的训练通常基于大量的采样数据集。

然而，某些样本的重要性可能高于其他样本，它们对模型的训练结果更具影响力。

因此，传统的随机采样方法可能会在采样过程中忽略掉一些重要的样本，从而导致训练效率低下。

重要性采样通过为各个样本赋予不同的采样权重，提高了对重要样本的采样概率，从而更有效地探索样本空间。

在深度学习中，重要性采样的应用可以通过两种主要方式来实现：重要性采样训练和重要性采样调整。

首先，重要性采样训练是一种基于重要性采样的模型训练方法。

它通过调整样本的权重来降低对低重要性样本的关注，同时增加对高重要性样本的关注。

这样一来，模型将更有可能学习到那些具有更大贡献的样本特征，从而提高模型的学习效率。

重要性采样训练可以应用于深度学习中的各个阶段，包括数据预处理、模型训练和优化等。

其次，重要性采样调整是一种基于重要性采样的模型参数更新方法。

在传统的梯度下降算法中，每个样本的梯度都被视为具有相同的重要性。

而重要性采样调整方法则根据每个样本的采样权重，调整对应的梯度，使得对于更重要的样本，其梯度对模型参数的更新更有贡献。

通过这种方式，模型能够更有效地更新参数，从而加快模型的收敛速度，提高学习效率。

此外，重要性采样还可以与其他技术相结合，以进一步提高深度学习模型的学习效率。

例如，与自适应采样方法结合使用，可以根据每个样本的重要性动态调整采样概率，从而更好地平衡采样效率和样本质量。

另外，与优化方法相结合，例如基于梯度的优化方法，可以更好地利用重要性采样的信息，加速模型的学习过程。

International Journal of Approximate Reasoning

Dynamic importance sampling inBayesian networks based on probability treesq Serafı´n Moral a ,Antonio Salmero ´n b,*a Department Computer Science and Artiﬁcial Intelligence,University of Granada,Avda.Andalucı´a 38,18071Granada,Spain b Department Statistics and Applied Mathematics,University of Almerı´a,La Can ˜ada de San Urbano s/n,04120Almerı´a,Spain Received 1February 2004;received in revised form 1April 2004;accepted 1May 2004Available online 17September 2004AbstractIn this paper we introduce a new dynamic importance sampling propagation algorithm for Bayesian networks.Importance sampling is based on using an auxiliary sampling distribution from which a set of conﬁgurations of the variables in the network is drawn,and the perform-ance of the algorithm depends on the variance of the weights associated with the simulated conﬁgurations.The basic idea of dynamic importance sampling is to use the simulation of a conﬁguration to modify the sampling distribution in order to improve its quality and so reduc-ing the variance of the future weights.The paper shows that this can be achieved with a low computational eﬀort.The experiments carried out show that the ﬁnal results can be very good even in the case that the initial sampling distribution is far away from the optimum.Ó2004Elsevier Inc.All rights reserved.Keywords:Bayesian networks;Probability propagation;Approximate algorithms;Importance sampling;Probability trees0888-613X/$-see front matter Ó2004Elsevier Inc.All rights reserved.doi:10.1016/j.ijar.2004.05.005qThis work has been supported by the Spanish Ministry of Science and Technology,project Elvira II (TIC2001-2973-C05-01and 02).*Corresponding author.Tel.:+34950015669;fax:+34950015167.E-mail addresses:smc@decsai.ugr.es (S.Moral),antonio.salmeron@ual.es (A.Salmero´n).International Journal of Approximate Reasoning38(2005)245–261/locate/ijar246S.Moral,A.Salmero´n/Internat.J.Approx.Reason.38(2005)245–2611.IntroductionIn this paper we propose a new propagation algorithm for computing marginal conditional probabilities in Bayesian networks.It is well known that this problem is NP-hard even if only approximate values are required[7].It means that it is always possible toﬁnd examples in which polynomial approximate algorithms pro-vide poor results,especially if the distributions contain extreme probabilities:there is a polynomial approximate algorithm if all the probabilities are strictly greater than zero[8],but its performance quickly deteriorates when the probabilities approach to zero.There exist several deterministic approximate algorithms[1–5,13,16,20,21]as well as algorithms based on Monte Carlo simulation.The two main approaches are: Gibbs sampling[12,15]and importance sampling[6,8,10,11,18,19,22].A class of these simulation procedures is composed by the importance sampling algorithms based on approximate pre-computation[11,18,19].These methods per-formﬁrst a fast but non-exact propagation,consisting of a node removal process [23].In this way,an approximateÔa posterioriÕdistribution is obtained.In the second stage a sample is drawn using the approximate distribution and the probabilities are estimated according to the importance sampling methodology[17].In this paper we start oﬀwith the algorithm based on approximate pre-computa-tion developed in[18].One of the particularities of that algorithm is the use of prob-ability trees to represent and approximate probabilistic potentials.Probability trees have the ability of approximating in an asymmetrical way,concentrating more re-sources(more branching)where they are more necessary:higher values with more variability(see[18]for a deeper discussion on these issues).However,as pointed out in[5],one of the problems of the approximate algorithms in Bayesian networks is that sometimes theﬁnal quality of an approximate potential will depend on all the potentials,including those which are not needed to remove the variable when per-forming exact propagation.Imagine that weﬁnd that,after deleting variable Z, the result is a potential that depends on variable X,and weﬁnd that this dependence is meaningful(i.e.the values of the potential are high and diﬀerent for the diﬀerent cases of X).If there is another potential not considered at this stage,in which all the cases of X except one have assigned a probability equal to zero,then the discrimina-tion on X we have done when deleting Z is completely useless,sinceﬁnally only one value of X will be possible.This is an extreme situation,but it illustrates that even if the approximation is carried out locally,the quality of theﬁnal result will depend on the global factors.There are algorithms that take into account this fact,as Markov Chain Monte Carlo,the Penniless propagation method presented in[5],and the Adaptive Importance Sampling(AIS-BN)given in[6].In this work,we improve the algorithm proposed in[18]allowing to modify the approximate potentials(the sampling distribution)taking as basis the samples ob-tained during the simulation.If samples with very small weights are drawn,the algo-rithm detects the part of the sampling distribution(which is represented as an approximate probability tree)that is responsible of this fact,and it is updated in such a way that the same problem will not occur in the next simulations.Actually,this is away of using the samples to obtain the necessary information to improve the quality of the approximations taking into account other potentials in the problem.Trees are very appropriate for this task,as they allow to concentrate more eﬀorts in the most necessary parts,i.e.in the conﬁgurations that were more frequently obtained in past simulations and for which the approximation was not good.The rest of the paper is organised as follows:in Section2it is described how prob-ability propagation can be carried out using the importance sampling technique.The new algorithm,called dynamic importance sampling,is described in Section3.In Sec-tion4the performance of the new algorithm is evaluated according to the results of some experiments carried out in large networks with very poor initial approxima-tions.The paper ends with conclusions in Section5.2.Importance sampling in Bayesian networksThroughout this paper,we will consider a Bayesian network in which X={X1,...,X n}is the set of variables and each variable X i takes values on aﬁnite set X i.If I is a set of indices,we will write X I for the set{X i j i2I},and X I will denote the Cartesian product·i2I X i.Given x2X I and J I,x J is the element of X J ob-tained from x by dropping the coordinates not in J.A potential f deﬁned on X I is a mapping f:X I!Rþ0,where Rþis the set of non-negative real numbers.Probabilistic information will always be represented by means of potentials,as in[14].The set of indices of the variables on which a potential f is deﬁned will be denoted as dom(f).The conditional distribution of each variable X i,i=1,...,n,given its parents in the network,X pa(i),is denoted by a potential p i(x i j x pa(i))for all x i2X i and x pa(i)2 X pa(i).If N={1,...,n},the joint probability distribution for the n-dimensional ran-dom variable X can be expressed aspðxÞ¼Yi2N piðx i j x paðiÞÞ8x2X N:ð1ÞAn observation is the knowledge about the exact value X i=e i of a variable.The set of observations will be denoted by e,and called the evidence set.E will be the set of indi-ces of the variables observed.The goal of probability propagation is to calculate theÔa posterioriÕprobabilityfunction pðx0k j eÞ,for all x0k2X k,for every non-observed variable X k,k2N n E.No-tice thatpðx0k j eÞ¼pðx0k;eÞ8x0k2X kand,since pðeÞ¼Px0k2X kpðx0k;eÞ,we can calculate the posterior probability if we com-pute the value pðx0k ;eÞfor every x0k2X k and normalise afterwards.Let H={p i(x i j x pa(i))j i=1,...,n}be the set of conditional potentials.Then,pðx0k ;eÞcan be expressed asS.Moral,A.Salmero´n/Internat.J.Approx.Reason.38(2005)245–261247pðx0k ;eÞ¼Xx2X Nx E¼ex k¼x0kYi2Npiðx i j x paðiÞÞ¼Xx2X Nx E¼ex k¼x0kYf2Hfðx domðfÞÞ8x0k2X k:ð2ÞIf the observations are incorporated by restricting potentials in H to the observed values,i.e.by transforming each potential f2H into a potential f e deﬁned on domðfÞn E as f e(x)=f(y),where ydomðfÞn E¼x,and y i=e i,for all i2E,then we have,pðx0k ;eÞ¼Xx2X Nx k¼x0kYf e2Hf eðx domðfeÞÞ¼Xx2X NgðxÞ8x0k2X k;ð3ÞwheregðxÞ¼Qf e2Hf eðx domðfeÞÞif x k¼x0k; 0otherwise:Thus,probability propagation conveys the estimation of the value of the sum in(3), and here is where the importance sampling technique is used.Importance sampling is well known as a variance reduction technique for estimating integrals by means of Monte Carlo methods(see,for instance,[17]),consisting of transform-ing the sum in(3)into an expected value that can be estimated as a sample mean. To achieve this,consider a probability function pÃ:X N![0,1],verifying that pÃ(x)>0for every point x2X N such that g(x)>0.Then formula(3)can be written aspðx0k ;eÞ¼Xx2X N;gðxÞ>0gðxÞpÃðxÞpÃðxÞ¼EgðXÃÞpÃðXÃÞ8x0k2X k;ð4Þwhere XÃis a random variable with distribution pÃ(from now on,pÃwill be called thesampling distribution).Then,if f xðjÞg mj¼1is a sample of size m drawn from pÃ,for eachx0k2X k,^pðx0k ;eÞ¼1mX mj¼1gðxðjÞÞpÃðxðjÞÞð5Þis an unbiased estimator of pðx0k;eÞwith varianceVarð^pðx0k ;eÞÞ¼1mXx2X Ng2ðxÞpÃðxÞ!Àp2ðx0k;eÞ!:ð6ÞThe value w j=g(x(j))/pÃ(x(j))is called the weight of conﬁguration x(j).Minimising the error of an unbiased estimator is equivalent to minimising its var-iance.As formulated above,importance sampling requires a diﬀerent sample to esti-mate each one of the values x0k of X k.However,in[18]it was shown that it is possibleto use a single sample(i.e.a single set of conﬁgurations of the variables X N n E)toestimate the probability for all the values x0k .In such case,the minimum variance isreached when the sampling distribution,pÃ(x),is proportional to g(x).In such case, 248S.Moral,A.Salmero´n/Internat.J.Approx.Reason.38(2005)245–261the weights are equal to p (e )for all the conﬁgurations and the variance of the esti-mation of the conditional probability for each x 0k 2X k is:Var ð^p ðx 0k j e ÞÞ¼1mðp ðx 0k j e Þð1Àp ðx 0k j e ÞÞ:This provides very good estimations depending on the value of m (analogously to the estimation of binomial probabilities from a sample),but it has the diﬃculty that it is necessary to handle p (x j e ),the distribution for which we want to compute the mar-ginals.Thus,in practical situations the best we can do is to obtain a sampling distri-bution as close as possible to the optimal one.Once p Ãis selected,p ðx 0k ;e Þfor each value x 0k of each variable X k ,k 2N n E can be estimated with the following algorithm:Importance Sampling(1)For j :=1to m (sample size)(a)Generate a conﬁguration x (j )2X N using p Ã.(b)Calculate the weight:w j :¼Q f 2H f e ðx ðj Þdom ðf e ÞÞp Ãðx ðj ÞÞ:ð7Þ(2)For each x 0k 2X k ,k 2N n E ,compute ^pðx 0k ;e Þas the sum of the weights in for-mula (7)corresponding to conﬁgurations containing x 0k divided by m .(3)Normalise the values ^p ðx 0k ;e Þin order to obtain ^p ðx 0k j e Þ.The sampling distribution for each variable can be obtained through a process of eliminating variables in the set of potentials H .An elimination order r is considered and variables are deleted according to such order:X r (1),...,X r (n ).The deletion of a variable X r (i )consists of marginalising it out from the combina-tion of all the functions in H which are deﬁned for that variable.More precisely,the steps are as follows:•Let H r (i )={f 2H j r (i )2dom(f )}.•Calculate f r ði Þ¼Q f 2H r ði Þf and f 0r ði Þdeﬁned on dom(f r (i ))n {r (i )},by f 0r ði Þðy Þ¼P x r ði Þf r ði Þðy ;x r ði ÞÞfor all y 2dom(f r (i ))n {r (i )},x r (i )2X r (i ).•Transform H into H n H r ði Þ[f f 0r ði Þg .Simulation is carried out in an order contrary to the one in which variables are deleted.To obtain a value for X r (i ),we will use the function f r (i )obtained in the dele-tion of this variable.This potential is deﬁned for the values of variable X r (i )and other variables already sampled.The potential f r (i )is restricted to the already ob-tained values of variables in dom(f r (i ))n {r (i )},giving rise to a function which depends only on X r (i ).Finally,a value for this variable is obtained with probability propor-tional to the values of this potential.If all the computations are exact,it was proved in [11]that we are really sampling with the optimal probability p Ã(x )=p (x j e ).S.Moral,A.Salmero ´n /Internat.J.Approx.Reason.38(2005)245–261249However,the result of the combinations in the process of obtaining the sampling distributions may require a large amount of space to be stored,and therefore approximations are usually employed,either using probability tables[11]or proba-bility trees[18]to represent the distributions.Instead of computing the exact poten-tials we calculate approximate ones with much fewer values.Then the deletion algorithm is faster and the potentials need less space.The price to pay is that the sampling distribution is not the optimal one and the accuracy of the estimations will depend on the quality of the approximations.The way in which a probabilistic potential can be approximated by a probability tree is illustrated in1.In[11]an alternative procedure to compute the sampling distribution was used. Instead of restricting f r(i)to the values of the variables already sampled,all the func-tions in H r(i)are restricted,resulting in a set of functions depending only on X r(i). The sampling distribution is then computed by multiplying all these functions.If the computations are exact,then both distributions are the same,as restriction and combination commute.When the combinations are not exact,generally the op-tion of restricting f r(i)is faster and the restriction of functions in H r(i)is more accu-rate,as there is no need to approximate the result of the combination of functions depending only on one variable,X r(i).3.Dynamic importance samplingDynamic importance sampling follows the same general structure as our previous importance sampling algorithms but with the diﬀerence that sampling distributions can change each time a new conﬁguration x(j)is simulated.The algorithm follows the option of restricting the functions in H r(i)before combining them when computing the sampling distribution for X r(i).Any conﬁguration of valuesðxðjÞrð1Þ;...;xðjÞrðnÞÞ,is simulated in reverse order,as in theoriginal importance sampling algorithm:Starting with xðjÞrðnÞandﬁnishing with xðjÞrð1Þ.Assume that we have already simulated the values c j i¼ðxðjÞrðnÞ;...;xðjÞrðiþ1ÞÞand thatwe are going to simulate a value xðjÞrðiÞfor X r(i).Let us denote by fc jithe result ofrestricting potential f to the values of c j i,and let f0rðiÞbe the function that was com-puted when removing variable X r(i)in the elimination algorithm(i.e.the result ofsumming the combination of the potentials containing X r(i)over all the possible val-ues of that variable).The procedure to simulate xðjÞrðiÞmakes some additional computations in order toassess the quality of the sampling distribution.More precisely the following elements are computed:•ðH rðiÞÞc ji ¼f fc jij f2H rðiÞg:The result of restricting all the functions in H r(i)to thevalues already simulated.•q r(i):The result of the combination of all the functions inðH rðiÞÞc ji .This functioncan be represented as a vector depending only on variable X r(i).•xðjÞrðiÞ:The simulated value for X r(i)which is obtained by drawing a value with aprobability proportional to the values of vector q r(i).b rðiÞ¼Px rðiÞqrðiÞðx rðiÞÞ:Thenormalisation value of vector q r(i).•a r(i):The value of potential f0rðiÞwhen instantiated for the cases in c j i.The dynamic algorithm we propose is based on the next theorem,which states that,if no approximations have been made,then b r(i)must be equal to a r(i).Theorem1.Let a r(i)and b r(i)be as deﬁned above.If during the elimination process all the trees have been computed exactly(i.e.none of them has been pruned),then it holds thata rðiÞ¼b rðiÞ:Proof.b r(i)is obtained by restricting the potentials in H r(i)to c j i¼ðxðjÞrðnÞ;...;xðjÞrðiþ1ÞÞ,combining them afterwards,and summing out the variable X r(i).On the other hand,a r(i)is the result of combining the potentials in H r(i),summing out X r(i)from the combined potential,and restricting the result to c j i.f0 rðiÞis computed by combining the potentials in H r(i)and then summing out X r(i).It means that the computations of a r(i)and b r(i)involve the same operations but in a different order:The restriction to conﬁguration c j i is done at the beginning for b r(i) and at the end for a r(i).Nevertheless,if all the computations are exact the results should be the same,since combination and restriction trivially commute for exact trees.hHowever,combination and restriction do not commute if the potentials involved have been previously pruned,since one of the pruned values may correspond to con-ﬁguration c j i.b r(i)is the correct value,since in this case the restriction is evaluated before com-bining the potentials,and thus,no approximation is made when computing it.Whilst,a r(i)is the value that can be found in potential f0rðiÞ,which is combined,and eventually pruned,before being evaluated for c j i.Potential f0rðiÞis the one thathas been used to compute the sampling probabilities of variables XðjÞrðnÞ;...;XðjÞrðiþ1Þ.Therefore,if b r(i)and a r(i)are very diﬀerent,it means that conﬁguration c j i has been S.Moral,A.Salmero´n/Internat.J.Approx.Reason.38(2005)245–261251drawn with a probability of occurrence far away from its actual value.The worst sit-uation is met when a r(i)is much greater than b r(i).For example,assume an extreme scenario in which b r(i)is equal to zero and a r(i)is large.Then we would be obtaining, with high probability,a conﬁguration that should never be drawn(its real probabil-ity is zero).1This fact would produce negative consequences,because the weights of all these conﬁgurations would be zero and therefore they would be completely useless.If instead of zero values,the exact probability were very small,there would be a similar scenario,but now the weights would be very small,and the real impact of these conﬁgurations in theﬁnal estimation would not be signiﬁcant.Summing up, we would be doing a lot of work with very little reward.Dynamic importance sampling computes the minimum of the values a r(i)/b r(i)and b r(i)/a r(i),considering that this minimum is equal to one if a r(i)=0.If this value is lessthan a given threshold,then potential f0rðiÞis updated to the exact value b r(i)for thegiven conﬁguration c j i¼ðxðjÞrðnÞ;...;xðjÞrðiþ1ÞÞ.This potential will be used in the nextsimulations,and thus c j i will be drawn with a more accurate probability in the future. If,for example,b r(i)is zero,it will be impossible to obtain it again.Updating the potential does not simply mean to change the value a r(i)by the new value b r(i).The reason is that we should do it only for conﬁguration c j i and a single value on a tree aﬀects to more than one conﬁguration(if the branch corresponding to that conﬁguration has been pruned and some variables do not appear)and then we may be changing the values of other conﬁgurations diﬀerent to c j i.If b r(i)=0,we could even introduce zeros where the real exact value is positive,thus violating the basic property of importance sampling which says that any possible conﬁguration must have a chance to be drawn.For instance,assume that the branches in a tree corresponding to conﬁgurations c1and c2lead to leaves labeled with numbers0 and0.1respectively.Now consider that the tree is pruned replacing both branches by a single number,for instance,0.05.In this case,if during the simulation it is found out that conﬁguration c1should be labeled with0,if we just replaced the value0.05 by0we would be introducing a false zero for conﬁguration c2.In order to avoid the insertion of false zeroes,we must branch the tree represent-ing f0rðiÞin such a way that we do not change its value for conﬁgurations for whichb r(i)is not necessarily the actual value.Therefore,the basic problem is to determine a subset of variables{X r(n),...,X r(i+1)},for which we have to branch the node of thetree associated with f0rðiÞso that only those leaves corresponding to the values of thesevariables in c j i are changed to the new value.Theﬁrst step is to consider the subset of active variables,A r(i)associated withpotential f0rðiÞ.This set represents the variables for which f0rðiÞshould be deﬁned ifcomputations are exact,but potentials are represented by probability trees which are pruned without error when possible(a node such that all its children are leaves with the same value is replaced by a single leaf with that value).1If we had stored in f0rðiÞthe exact value(zero),then,as this value is used to simulate the values of(X r(n),...,X r(i+1)),the probability of this conﬁguration should have been zero.252S.Moral,A.Salmero´n/Internat.J.Approx.Reason.38(2005)245–261This set is computed during the variable elimination phase.Initially,A r(i)is the un-ion of the domains of all the potentials in H r(i)minus X r(i),which is the set of variablesof potential f0rðiÞif we would have applied a deletion algorithm with potentials repre-sented by probability tables.But this set can be further reduced:If a variable,say X j,can be pruned without error from f0rðiÞ(i.e.for every conﬁguration of the other vari-ables,f0rðiÞis constant on the values of X r(i))and all the potentials in H r(i)containingthis variable have been calculated in an exact way(all the previous computations have only involved pruning without error)then X j can be removed from A r(i).Though this may seem atﬁrst glance a situation diﬃcult to appear in practice,it happens for all the variables for which there are not observed descendants[18].All these variables can be deleted in an exact way by pruning the result to the constant tree with value1.0and this provides an important initial simpliﬁcation.Taking A r(i)as basis,we consider the tree representing f0rðiÞand follow the pathcorresponding to conﬁguration c j i(selecting for each variable in a node the child cor-responding to the value in the conﬁguration)until we reach a leaf.Let L be the label of that leaf and B r(i)be the set of all the variables in A r(i)which are not in the branch of the tree leading to leaf L.The updating is carried out according to the following recursive procedure:Procedure Update(L,a r(i),b r(i),B r(i))1.If B r(i)=;,2.Assign value b r(i)to leaf L3.Else4.Select a variable Y2B r(i)5.Remove Y from B r(i)6.Branch L by Y7.For each possible value y of Y8.If y is not the value of Y in c j i9.Make the child corresponding to y be a leaf with value a r(i)10.Else11.Let L y be the child corresponding to value y12.Update(L y,a r(i),b r(i),B r(i))In this algorithm,branching a node by a variable Y consists of transforming it into an interior node with a child for each one of the values of the variable.The idea is tobranch as necessary in order to be possible to change the value of f0rðiÞonly for thevalues of active variables A r(i)in conﬁguration c j i,leaving the values of this potential unchanged in other cases.Imagine the case of Fig.2,in which we have arrived to the leaf in the left with a value of a r(i)=0.4.Assume also that the variables in B r(i)are X, Y and Z,each one of them taking values in{0,1}and that the values of these variables in the current conﬁguration are1,0and1respectively.Finally,consider that we have to update the value of this conﬁguration in the tree to the new value b r(i)=0.6.The result is the tree in the right side of Fig.2.Observe that the order in which variables are selected in Step4is not relevant,since at the end all the variables in B r(i)are in-cluded and the sizes of the trees resulting from diﬀerent orders are the same.S.Moral,A.Salmero´n/Internat.J.Approx.Reason.38(2005)245–261253It must be pointed out that,unlike standard importance sampling,in the dynamic algorithm that we propose,the conﬁgurations in the sample are not independent,since the sampling distribution used to draw a conﬁguration may be modiﬁed according to the conﬁgurations previously simulated.However,the resulting estima-tor remains unbiased,as stated in the next theorem.Theorem 2.Let X k be a non-observed variable and e a set of observations.Then,for each x 0k 2X k ,the dynamic importance sampling estimator of p ðx 0k ;e Þ,denoted as ^p ðx 0k ;e Þ,is unbiased.Proof.Assume that the sampling distribution,p Ã,has been updated l times,and let p Ãi ,i =1,...,l ,denote the l sampling distributions actually used in the simulation process.Given a sample S ={x (1),...,x (m )},let S i ,i =1,...,l ,denote the elements in S drawn from p Ãi .Then,according to Eq.(5)^p ðx 0k ;e Þ¼1m X m j ¼1g ðx ðj ÞÞp Ãðx ðj ÞÞ¼1m X l i ¼1X x 2S i g ðx Þp i ðx Þ:According to Eq.(4),for a ﬁxed p Ãi ,E ½g ðx Þ=p Ãi ðx Þ ¼p ðx 0k ;e Þ,which means thatg ðx Þ=p Ãi ðx Þis an unbiased estimator of p ðx 0k ;e Þ.Therefore,^p ðx 0k ;e Þis the average of m unbiased estimators of p ðx 0k ;e Þ,and thus ^p ðx 0k ;e Þis an unbiased estimator of p ðx 0k ;e Þ.hThough all the cases in the sample are not independent,this does not imply that the ﬁnal variance is higher than when using independent samples.We must take into account that the dependence lies in the selection of the distribution to sample succes-sive conﬁgurations,but once this distribution is ﬁxed,then the conﬁguration is inde-pendent of the previous ones.In order to show that this reasoning is correct,we are going to simplify the scenario by considering a simple change of distribution instead of several distributions.This result can be easily extended to the generalcase.254S.Moral,A.Salmero´n /Internat.J.Approx.Reason.38(2005)245–261。

Reconciliation importance of good sampling and QAQC Noppe 2004

Reconciliation: importance of good sampling and data QA-QC1Mark NoppéDirector and Principal Consultant GeologistSnowden Mining Industry Consultants Pty LtdPO Box 2207BrisbaneQueensland 4001AustraliaAbstractConsider the following statements (Harry and Schroeder, 2000):- You don’t know what you don’t know- You don’t measure what you don’t value- You can’t value what you don’t measure- If you can’t measure it you can’t control it- If you can’t control it you can’t improve itThese comments about business and operational control are very applicable to mine reconciliation, and particularly the input sampling estimates and measurements. Understanding, quantifying, controlling and correctly reporting these results is an integral part of successfully monitoring the performance of the mining operation.IntroductionMining reconciliation is the comparison of estimated tonnage, grade and metal with actual measurements. The aims are to measure the performance of the operation, support the calculation of the mineral asset, validate the Mineral Resource and Ore Reserve estimates, and provide key performance indicators for short and long-term control (Morley, 2003). On-going, regular and efficient reconciliation should also highlight improvement opportunities and allow for proactive short-term forecasting by providing reliable calibrations to critical estimates. The concept is that of “measure, control and improve”.Meaningful reconciliationMany operations have a reconciliation process in place, although most function on (or are only reliable) on a long-term basis – often because of the time and effort to collate and report the data from disparate databases across multiple function areas. The aim should be to minimize multiple handling of the data, with a centralised reporting platform, an example of which is outlined in Figure 1. Operators often overlook the ‘volume-variance’ effect – namely that the larger the tonnage or time increment that is examined the less variable the results will be. The time period over which the reconciliation is reported is important to ensure that the results are meaningful and have the desired level of associated confidence.XYZ, EGRU Contribution No 62, 2004Figure 1 Schematic illustration of a reconciliation system (after Morley, 2003)The usefulness of the reconciliation data, however, remains dependent on the quality and reliability of the input data, namely the estimates and the measurements. The resource and reserve estimates are themselves dependent on the underlying sample data and the processes used to generate the resource and reserve estimates (including short-term grade control estimates). The mining and processing measurements include survey, belt samples, on-line analysers, weightometers and flow-meters. All of these measurements have somedegree of associated error or confidence level. The key elements of a reconciliation processare summarized in Figure 1, whilst some of the variables that affect the reliability of reconciliation results are presented in Table 1.XYZ, EGRU Contribution No 62, 2004Figure 1 Schematic illustration of the mining reconciliation process and key issues for analysis (after Morley, 2003)Geological model causesTrue in situ nugget effect Sampling and subsampling errors Analytical errorsEstimation errors Mining causesM ining model parallel to cross mineralisation in open pitDisplacement of mineralization boundaries upon blastingSketchley, D A, 1999. Gold deposits: establishing sampling protocols and monitoring quality control. Explor. Mining Geol., Vol 7, Nos 1 and 2, Canadian Institute of Mining, Metallurgy and Petroleum, pp 129-138.Mark Noppé is a Director of Snowden Mining Industry Consultants Pty Limited (Australia) and Manager of Brisbane office. He has more than 17 years experience in exploration, mining geology, mineral resource estimation and management gained with Anglo American and Snowden. Mark has a wide range of geological expertise, ranging from technical review, due diligence, sampling and reconciliation, resource estimation, and feasibility studies, to training and facilitation. Mark's experience covers a range of commodities in a variety of geological and geographic locations, including: coal; gold; sulphide and laterite nickel; copper, cobalt, zinc and lead; bauxite, phosphate and potash; PGE and diamonds in Africa, UK, Middle East, Central Asia, CIS, Indonesia and Australia.XYZ, EGRU Contribution No 62, 2004。

机器学习论文

A Framework for Quality Assurance of Machine Learning Applications Christian Murphy Gail Kaiser Marta AriasDept. of Computer Science Columbia UniversityNew York, NY cmurphy@ Dept. of Computer ScienceColumbia UniversityNew York, NYkaiser@Center for ComputationalLearning SystemsColumbia UniversityNew York, NYmarta@AbstractSome machine learning applications are intended to learn properties of data sets where the correct answers are not already known to human users. It is challenging to test and debug such ML software, because there is no reliable test oracle. We describe a framework and collection of tools aimed to assist with this problem. We present our findings from using the testing framework with three implementations of an ML ranking algorithm (all of which had bugs).1. IntroductionWe investigate the problem of making machine learning (ML) applications dependable, focusing on software quality assurance. Conventional software engineering processes and tools do not always neatly apply: in particular, it is challenging to detect subtle errors, faults, defects or anomalies (henceforth “bugs”) in those ML applications where there is no reliable test “oracle”. The general class of software systems with no reliable test oracle available is sometimes known as “non-testable programs” [1].We are specifically concerned with ML applications addressing ranking problems, as opposed to the perhaps better-known classification problems. When such applications are applied to real-world data (or, for that matter, to “fake” data), there is typically no easy way to determine whether or not the program’s output is “correct” for the input. In general, there are two phases to “supervised” machine learning – the first where a training data set with known positive or negative labels is analyzed, and the second where the results of that analysis (the “model”) are applied to another data set where the labels are unknown; the output of the latter is a ranking, where when the labels become known, it is intended that those with a positive label should appear as close to the top of the ranking as possible given the information known when ranked. (More accurately, labels are non-negative numeric values, and ideally the highest valued labels are at or near the top of the ranking, with the lowest valued labels at or near the bottom.) Formal proofs of an ML ranking algorithm’s optimal accuracy do not guarantee that an application implements or uses the algorithm appropriately, and thus software testing is needed.In this paper, we describe a framework supporting testing and debugging of supervised ML applications that implement ranking algorithms. The current version of the framework consists of a collection of modules targeted to several ML implementations of interest, including a test data set generator; tools to compare the output models and rankings; several trace options inserted into the ML implementations; and utilities to help analyze the traces to aid in debugging.We present our findings to date from a case study concerning the Martingale Boosting algorithm, which was developed by Long and Servedio [2] initially as a classification algorithm and then adapted by Long and others [3] into a ranking algorithm. “MartiRank” was a nice initial target for our framework since the algorithm is relatively simple and there were already three distinct, actively maintained implementations developed by different groups of programmers.2. Background2.1. Machine learning applicationsPrevious and ongoing work at the Center for Computational Learning Systems (CCLS) has focused on the development of ML applications like the system illustrated in Figure 1 [3]. The goal of that system, commissioned by Consolidated Edison Company ofNew York, is to rank the electrical distribution feeders most susceptible to impending failure with sufficient accuracy so that timely preventive maintenance can be taken on the right feeders at the right time. The prospective users would like to reduce feeder failure rates in the most cost effective manner possible. Scheduled maintenance avoids risk, as work is done when loads are low, so the feeders to which load is shifted continue to operate well within their limits. Targeting preventive maintenance to the most at-risk feeders (those at or near the top of the ranking) offers huge potential benefits. In addition, being able to predict incipient failures in close to real-time can enable crews and operators to take short-term preventative actions (e.g., shifting load to other, less loaded feeders). However, the ML application must be quite dependable for an organization to trust its results sufficiently to thusly deploy expensive resources.Other ML algorithms have also been investigated, such as Support Vector Machines (SVMs) [4] and linear regression, as the basis for the ML Engine of the example system and other analogous applications. However, much of the CCLS research has focused on MartiRank because, in addition to producing good results, the models it generates are relatively easy to understand and sometimes “actionable”. That is, it is clear which attributes from the input data most contributed to the model and thus the output ranking.In some cases the values of those attributes might then be closely monitored and/or externally adjusted.This example ML application is presented elsewhere [3]. The purpose of this paper is to present the framework we developed for testing and debugging such applications, with the goal of making them more dependable. The framework is written in Python on Linux. Our initial results reported here focus on the MartiRank implementations.One complication in this effort arose due to conflicting technical nomenclature: “testing”, “regression”, “validation”, “model” and other relevant terms have very different meanings to machine learning experts than they do to software engineers. Here we employ the terms “testing” and “regression testing” as appropriate for a software engineering audience, but we adopt the machine learning sense of “model” (i.e., the rules generated during training on a set of examples) and “validation” (measuring the accuracy achieved when using those rules to rank the training data set, rather than a different data set).2.2. MartiRank algorithmThe algorithm is shown in Figure 2 [3]. The pseudo-code presents it as applied to feeder failures, where the label indicates the number of failures (zero meaning the feeder never failed); however, the algorithm could be applied to any attribute-value data set labeled with non-negative values. In each round of MartiRank, the set of training data is broken into sub-lists (there are N sub-lists in the N th round, each containing 1/N th of the total number of failures). For each sub-list, MartiRank sorts that segment by each attribute, ascending and descending, and chooses the attribute that gives the best “quality”. For quality comparisons, the implementations all use a slight variant, adapted to ranking rather than classification, of the Area Under the receiver operating characteristic Curve (AUC) [5]. The AUC is a conventional quality metric employed in the ML community: 1.0 is the best possible, 0.0 is the worst possible, and 0.5 is random.In each round, the definition of each segment thus has three facets: the percentage of the examples from the original data set that are in the segment, the attribute on which to sort them, and the direction (ascending or descending) of the sort. In the model thatis generated, the N th round appears on the N th line of a plain-text file, with the segments separated by semicolons and the segment attributes separated by commas. For instance:0.4000,32,a;0.6500,12,d;1.0000,nopFigure 1. Incoming dynamic data is stored in the main database. The ML Engine combines this with static data to generate and update models, and then uses these models to create rankings, which can be displayed via the decision support app. Any actions taken as a result are tracked and stored in the database.might appear on the third line of the model file, representing the third round. This means that the first segment contains 40% of the examples in the data set and sorts them on attribute 32, ascending. The second segment contains the next 25% (65 minus 40) and sorts them on attribute 12, descending. The last segment contains the rest of the attributes and does a “NOP” (no-op), i.e., does not sort them again because the order resulting from the previous round had the best quality compared to re-sorting on any attribute.This model could then be re-applied to the training data (called “validation” in ML terminology) or applied to another, previously-unseen set of data (called the “testing data”). In either case, the output is a ranking of the data set examples and the overall quality of the entire ranked list can be calculated.2.3. MartiRank implementationsThe first of the three implementations was written in Perl, hereafter referred to as PerlMarti, as a straightforward implementation of the algorithm that included no optimizations. However, when applied to large data sets, e.g., thousands of examples with hundreds of attributes, PerlMarti is rather slow.A C version, hereafter CMarti, was written to improve performance (speed). CMarti also introduced some experimental options to try to improve quality.Another implementation also written in C, called FastCMarti, was designed to minimize the costly overhead of repeatedly sorting the attribute values. It sorted the full data set on each attribute at the beginning of an execution, before the first round, and remembered the results; it also used a faster sorting algorithm than CMarti (hence the name FastCMarti). This implementation also introduced some different experimental options from those in CMarti.2.4. Data setsThe MartiRank algorithm is based on sorting, with the implicit assumption that the sorted values are numerical. While in principle lexicographic sorts could be employed, non-numerical sorts do not seem intuitively appealing as ML predictors; for instance, it may not be meaningful to think of an electrical device manufactured by “Westinghouse” as more or less than something made by “General Electric” just because of their alphabetical ordering. Thus the implementations expect that all input data will be numerical.Though much of the real-world data of interest (from the system of Figure 1) indeed consists of numerical values – including floating point decimals, dates and integers – some of the data is instead categorical. Categorical data refers to attributes in which there are K different distinct values (typically alphanumeric as in the manufacturer example), but there is no sorting order that would be appropriate for the ranking algorithm. In these cases, a given attribute with K distinct values is expanded to K different attributes, each with two possible values: a 1 if the example has the corresponding attribute value, and a 0 if it does not. That is, amongst the K attributes, each example should have exactly one 1 and K-1 0’s.Some attributes in the real-world data sets need to be removed or ignored, for instance, because the values consist of free-text comments. Generally, these cannot be converted to values that can be meaningfully sorted.2.5. Related workAlthough there has been much work that applies machine learning techniques to software engineering and software testing [6, 7], there seems to be very little work in the reverse sense: applying software testing techniques to machine learning software, particularlyFigure 2: MartiRank Algorithm.those ML applications that have no reliable test oracle. Our framework builds upon Davis and Weyuker’s [8] approach to testing with a “pseudo-oracle” (comparing against another implementation of the specification), but most aspects of our framework are still useful even when there is just one implementation.There has been much research into the creation of test suites for regression testing [9] and generation of test data sets [10, 11], but not applied to ML code. Repositories of “reusable” ML data sets have been collected (e.g., the UCI Machine Learning Repository [12]) for the purpose of comparing result quality, but not for testing in the software engineering sense.Orange [13] and Weka [14] are two of the several frameworks that aid in developing ML applications, but the testing functionality they provide is again focused on comparing the quality of the results, not the “correctness” or dependability of the implementations.3. Testing Approach3.1. Optimization optionsCMarti and FastCMarti provide runtime options that turn on/off “optimizations” intended to improve result quality. These generally involve randomization (probabilistic decisions), yet it is challenging to evaluate test results when the outputs are not deterministic. Therefore, these options were disabled for all testing thus far: Our goal in comparing these implementations was not to get better results but to get consistent results.We initially believed that PerlMarti was a potential “gold standard” because it was truest to the algorithm as well as originally coded by the algorithm’s inventor, but as we shall see we found bugs in it, too. However, the fact that we had three implementations of MartiRank coded by different programmers helped immensely: we could generally assume that – with all options turned off – if two implementations agreed and the third did not, the third one was probably “wrong” (or, at least, we would know that something was amiss in at least one of them).3.2. Types of testingWe focused on two types of testing: comparison testing to see if all three implementations produced the same results, and regression testing to compare new revisions of a given implementation to previous ones (after bug fixes, refactorings, and enhancements to the optimization options).The data sets for some test cases were manually constructed, e.g., so that a hand-simulation of the MartiRank algorithm produced a “perfect” ranking, with all the positive examples (feeder failures) at the top and all the negative examples (non-failures) at the bottom. These data sets were very small, e.g., 10 examples each with 3 attributes.We also needed large data sets, to exercise a reasonable number of MartiRank rounds (the implementation default is 10) with still sufficiently many examples in each segment in the later rounds. We tested with some (large) real-world data sets, which generally have many categorical attributes, many repeating numerical values, and many missing values. However, in order to have more control over the test cases, e.g., to focus on boundary conditions from the identified equivalence classes, most of our large data sets were automatically generated with F failures (positive-labeled examples), N numerical attributes and K categorical attributes. F is any percentage between 0 and 100. The N numerical attributes were specified as including or not including any repeating values, with 0 to 100 percent missing values; the sets of values for each attribute were independent. For each of the K categorical attributes, the number of distinct values and the percent per category and missing were specified.3.3. Models versus rankingsOur evaluation of test outputs focused primarily on the models, as it is virtually always the case that if two versions produce two different models, then the rankings will also be different: if different models do produce the same rankings, that is likely by chance (i.e., an effect of the data set itself and not the model) and does not mean that the versions were producing “consistent” results. However, even when two implementations or revisions generate the same model, we cannot assume that the rankings will be the same: CMarti and PerlMarti generate rankings via programs that are separate from the code used to generate the models, so it is possible that differences could exist.FastCMarti does not follow the typical supervised ML convention in which a training data set is used to generate a model and then that model is given a separate “testing” data set with unknown labels to rank. Instead, the two data sets are joined together and each example marked accordingly. FastCMarti runs on the combined data set, but only the training data are used to create the model. The testing data are sorted and segmented along with the training data, and the final ranking of the testing data is the output – the model itself is merely a side effect that we needed to extract in order to compare across versions.4. Testing Framework4.1. Generating data setsWe created a tool that randomly generates values and puts them in the data set according to certain parameters. This allowed us to separately test different equivalence classes and ultimately create a suite of regression tests that covered those classes, focusing on boundaries. The parameters include the number of examples, the number of attributes, and the names of the output test data set files (which were produced in different formats for the different implementations).The data generation tool can be run with a flag that ensures that no values are repeated within the data set. This option was motivated by the need to run simple tests in which all values are different, so that sorting would necessarily be deterministic (no “ties”). It works as follows: for M attributes and N examples, generate a list of integers from 1 to M*N and then randomly shuffle them. The numbers are then placed into the data set. If the flag is not used, then each value in the data set is simply a random integer between 1 and M*N; there is thus a possibility that numbers may repeat, but this is not guaranteed.The utility is also given the percentage of failures to include in the data set. For all test cases discussed in this paper, each example could only have a label of 1 (indicating a failure) or 0 (non-failure). Similarly, a parameter specifies the percentage of missing values. Note that the label value is never missing.Lastly, parameters could be provided for generating categorical data (with K distinct values expanded to K attributes as described above). For creating categorical data, the input parameter to the data generation utility is of the format (a1, a2, ..., a K-1, a K, b), where a1 through a K represent the percentage distribution of those values for the categorical attribute, and b is the percent of unknown values. The utility also allows for having multiple categorical attributes, or for having none at all.4.3. Comparing modelsWe created a utility that compares the models and reports on the differences in each round: where the segment boundaries are drawn, the attribute chosen to sort on, and the direction. Typically, however, any difference between models in an earlier round would necessarily affect the rest of the models, so only the first difference is of much practical importance.4.4. Comparing rankingsAs explained above, we cannot simply assume that the same models will produce the same rankings for different implementations or revisions. This utility reports some basic metrics, such as the quality (AUC) for each ranking, the number of differences between the rankings (elements ranked differently), the Manhattan distance (sum of the absolute values of the differences in the rankings), and the Euclidean distance (in N-dimensional space). Another metric given is the normalized Spearman Footrule Distance, which attempts to explain how similar the rankings are (1 means that they are exactly the same, 0 means they are completely in the opposite order) [15]. Some of these metrics have mostly been useful when testing the “optimization” options, outside the scope of this paper.4.5. Tracing optionsThe final part of the testing framework is a tool for examining the differences in the trace outputs produced by different test runs. We added runtime options to each implementation to report significant intermittent values that arise during the algorithm’s execution, specifically the ordering of the examples before and after attempting to sort each attribute for a given segment, and the AUC calculated upon doing so. This is extremely useful in debugging differences in the models and rankings, as it allows us to see how the examples are being sorted (there may be bugs in the sorting code), what AUC values are determined (there may be bugs in the calculations), and which attribute the code is choosing as best for each segment/round (there may be bugs in the comparisons).5. Findings5.1. Testing with real-world dataWe first ran tests with some real-world data on all three implementations. Those data sets contained categorical data and both missing and repeating values. Our hope was that, with all “optimizations” disabled, the three implementations would output identical models and rankings.Not only did PerlMarti and FastCMarti produce different models, but CMarti reproducibly gave seg faults. Using the tracing utilities for the CMarti case, we found that some code that was only required for one of the optimization options was still being called even when that flag was turned off – but the internal state was inappropriate for that execution path. We refactored the code and the seg faults disappeared. However, the model then created by CMarti was still different from those created by either of the other two.These tests demonstrated the need for “fake” (controlled) data sets, to explore the equivalence classes of non-repeating vs. repeating values, none-missing vs. missing values, and non-categorical vs. categorical attributes (which are necessarily repeating).5.2. Simple comparison testingWe hand-crafted data sets (i.e., we did not yet use the framework to generate data sets) to see whether the implementations would give the same models in cases where a “perfect” ranking was possible. That is, we constructed data sets so that a manually-simulated sequence of sorting the segments (i.e., model) led to a ranking in which all of the failures were at the top and all the non-failures were at the bottom. It was agreed by the CCLS machine learning researchers that any implementation of MartiRank should be able to find such a “correct” model. And they generally did.In one of the “perfect” ranking tests, however, the implementations produced different results because the data set was already ordered as if sorted on the attribute that MartiRank would choose in the first round. In the reported models, CMarti sorted anyway, but PerlMarti and FastCMarti did NOPs because leaving the data as-is would yield the same quality (AUC).After consulting with the CCLS ML researchers, we “fixed” PerlMarti and FastCMarti so that they would always choose an attribute to sort on in the first round, i.e., never select NOP in the first round. The rationale was that one could not expect that the initial ordering of a real-world data set would happen to produce the best ranking in the first round, and any case in which the data are already ordered in a way that yields the “best” quality is likely just a matter of luck – so sorting is always preferable to not sorting. However, the MartiRank algorithm as defined in Figure 2 does not treat the first round specially, so the implementations now thus deviate from the algorithm.In another simple test, we wanted to see what would happen if sorting on two different attributes gave the same AUC. For instance, if sorting on attribute #3 ascending would give the same AUC as sorting on attribute #10 descending, and either provided the best AUC for this segment, which would the code pick? Our assumption was that the implementations should choose an attribute/direction for sorting only when it produces a better AUC than the best so far, starting with attribute #0 (leftmost in the data file) and going up to attribute #N (rightmost), as specified in MartiRank.This led to the interesting discovery that FastCMarti was doing the segmentation (sub-list splits) differently from PerlMarti and CMarti. By using the framework’s model analysis tool, we found that even when FastCMarti was choosing the same attribute to sort on as the other implementations, in the subsequent round the percentage of the data set in each segment could sometimes be different.It appeared (and we confirmed using the tracing analysis tool) that the difference was that FastCMarti was taking enough failure examples (labeled as 1s) to fill the segment with the appropriate number, and then taking all non-failure examples (0s) up to the next failure (1). In contrast, CMarti and PerlMarti took only enough failures to fill the segment and stopped there. For example, if the sequence of labels were:1 1 0 0 1 0 0 1 0 0and we were in the second round (two segments, each having ½ of the failures), then CMarti and PerlMarti would create segments like this:1 1 | 0 0 1 0 0 1 0 0but FastCMarti would create segments like this:1 1 0 0 | 1 0 0 1 0 0Both are “correct” because the algorithm merely says that, in the N th round, each segment should contain 1/N th of the failures, and here each segment indeed contains two of the four. The algorithm does not specify where to draw the boundaries between the non-failures. This is the first instance we found in which the MartiRank algorithm did not address an implementation-specific issue, which does not matter with respect to formal proofs, but does matter with respect to consistent testing.Once these issues were addressed, we repeated all the small test cases as well as with larger generated data sets, both for regression testing purposes (to ensure that the fixes did not introduce any new bugs) and for comparison testing (to ensure that all three implementations produced the same models).5.3. Comparison testing with repeating valuesThe next tests we performed with repeating values, that is, the same value could appear for a given attribute for different examples (in the real-world data sets, voltage level and activation date attributes involve many repeating values). We again started with small hand-crafted data sets that allowed us to judge the behavior by inspection. In one test, PerlMarti and CMarti found a “perfect” ranking after two rounds, but FastCMarti did not find one at all. In another test, PerlMarti/CMarti vs. FastCMarti showed different segmentations in a particular round.Then by using larger, automatically generated data sets, we confirmed our intuition that the CMarti and PerlMarti sorting routines were “stable” (i.e., theymaintain the relative order of the examples from the previous round when the values are the same), whereas FastCMarti was using a faster sorting algorithm that was not a stable sort (in particular producing a different order than a stable sort in the case of “ties”). Again, the algorithm did not address a specific implementation issue – which sorting approach to use – and different implementation decisions led to different results.After replacing FastCMarti’s sorting routine with a stable sort, we noticed that – again in an effort to be “fast” – the resulting list from the descending sort was simply the reverse of the list from the ascending sort, which does not retain the stability. For instance, if the stable ascending sort returned examples in this order:1 2 A B 5 6where A and B have the same values, then the stable descending sort should be:6 5 A B 2 1But FastCMarti was simply taking the reverse of the ascending list to produce:6 5 B A 2 1This code was “fixed”. This modification necessarily had an adverse effect on runtime, but provided the consistency we sought.5.4. Comparison testing of rankingsPreviously we had only compared the models. Now for the cases where the models were the same, we wanted to check whether the rankings were also identical. For CMarti and PerlMarti, ranking generation involved a separate program that we had not yet tested.We used the testing framework to create new large data sets with repeating values and used the analysis tool to analyze the rankings (at this point, all three implementations were producing the same models). CMarti and PerlMarti agreed on the rankings, but FastCMarti did not. The framework allowed us to determine how different, based on the various metrics such as normalized Spearman Footrule Distance and AUCs, as well as to determine why they were different, using the trace analysis tool.Using the tracing utility to see how the examples were being ordered during each sorting round, we found that the “stability” in FastCMarti was based on the initial ordering from the original data set, and not from the sorted ordering at the end of the previous round. That is, when a list that contained repeating values was to be sorted, CMarti and PerlMarti would leave those examples in their relative order as they stood at the end of the previous round, but FastCMarti would leave them in the relative order as they stood in the original data set. FastCMarti was designed this way to make it faster, i.e., by “remembering” the sort order for each attribute at the very beginning of the execution, and not having to re-sort in each round.For instance, a data set with entries A and B such that A appears in the set before B would look like: ....A....B....If in the first round MartiRank sorts on some attribute such that B gets placed in front of A, the ordering would then look like:....B....A....In the second round, if the examples are in the same segment and MartiRank sorts on some attribute that has the same value for those two examples, PerlMarti and CMarti would then end up like this:......BA......because B was before A at the end of round 1. However, FastCMarti would do this:......AB......because A was before B in the original data set.Since this was not explicitly addressed in the MartiRank algorithm, we contacted Long and Servedio, who agreed that remembering the order from the previous round was more in the spirit of the algorithm since it would take into account its execution history, rather than just the somewhat-randomness of how the examples were ordered in the original data set. Fixing this problem will require rethinking the entire approach to “fastness”, which has not yet occurred; thus all further comparison testing omitted FastCMarti.5.5. Comparison testing with sparse data setsOnce PerlMarti and CMarti were producing the same models for the cases with repeating values, we began to test data sets that had missing values. We used the framework to create large, randomly-generated (but non-repeating) data sets with percent of missing values as a parameter (0.5%, 1%, 5%, 10%, 20%, and 50%).In these tests, both implementations were initially generating different models, and there was no way to know which was “correct” since the MartiRank algorithm does not dictate how to handle missing values. Consulting with the CCLS ML researchers, we decided that the sorting should be “stable” with respect to missing values in that examples with a missing attribute value should remain in the same position, with the other examples (with known values) sorted “around” them. For instance, when the values:4 A5 2 1 B C 3are sorted in ascending order (with A, B and C representing the missing values), the result should be:1 A234 B C 5。

泰尔森估算法稳健非参数统计方法

泰尔森估算法稳健非参数统计方法泰尔森估算是通过选择通过成对点的所有线的斜率的中值来稳健地将线拟合到平面中的采样点（简单线性回归）的方法。

它也被称为Sen的斜率估计，斜率选择，单中值方法，Kendall鲁棒线拟合方法，和Kendall-Theil鲁棒线。

泰尔森估算（英文：Theil–Sen estimator）是通过选择通过成对点的所有线的斜率的中值来稳健地将线拟合到平面中的采样点（简单线性回归）的方法。

它也被称为Sen 的斜率估计，斜率选择，单中值方法，Kendall 鲁棒线拟合方法，和Kendall-Theil 鲁棒线。

它以Henri Theil 和Pranab K. Sen 命名，他们分别在1950 年和1968 年以及Maurice Kendall 之后发表了关于这种方法的论文。

该估计器可以有效地计算，并且对异常值不敏感。

对于偏斜和异方差数据，它可以比非鲁棒简单线性回归明显更准确，并且就统计功效而言，即使对于正态分布的数据也能很好地与非鲁棒最小二乘法竞争。

它被称为“用于估计线性趋势的最流行的非参数技术”。

根据Theil（1950）的定义，一组二维点的Theil-Sen 估计量是由所有样本对确定的斜率的中值m。

点。

Sen（1968）扩展了这个定义来处理两个数据点具有相同x 坐标的情况。

在Sen 的定义中，人们只采用仅具有不同x 坐标的点对定义的斜率的中值。

一旦确定了斜率m，就可以通过将y 截距b 设置为值yi-mxi 的中值来确定来自采样点的线。

正如Sen 观察到的那样，这个估计量是使得Kendall tau 秩相关系数比较xi 的值与第i 次观测的残差的值近似为零。

斜率估计的置信区间可以被确定为包含由点对确定的线的中间95%的斜率的区间，并且可以通过采样点对并且确定采样的95%间隔来快速估计。

连续下坡。

根据模拟，大约600 个样本对足以确定准确的置信区间。

Theil-Sen 估计量的变化，Siegel（1982）的重复中值回归，确定每个样本点，通过斜率的中间mi那一点，然后将整体估计量确定为这些中位数的中位数。

抽样方法与样本容量的确定

第七章抽样方法 Chapter 7 Sampling Methods
抽样是通过抽取总体中的部分单元，收集这些单元的信息，用来对作为整体的总体进行统计推断的一种手段。本章讨论了抽样的基本问题。 Sampling is a means of selecting a subset of units from a population for the purpose of collecting information for those units, usually to draw inference about the population as a whole.
非概率抽样的优点是： The advantages of non-probability sampling are that:

快速简便；费用相对较低；不需要抽样框；对探索性研究和调查的设计开发很有用。 It is quick and convenient It is relatively inexpensive It requires no sampling frame It can be useful for exploratory studies and survey development
抽样的两种主要类型是概率抽样与非概率抽样。 There are two types of sampling: nonprobability sampling and probability sampling
非概率抽样 non-probability 的用途是有限的，因为抽选单元的倾向性不允许对调查总体进行推断。然而非概率抽样快速简便，对探索性研究很有用，特别是在市场调查中应用非常广泛。
1.随意抽样Haphazard sampling

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。

Sampling中文解释

Sampling中文解释1．非概率抽样（Non-probability sampling）又称非随机抽样，指根据一定主观标准抽取样本，令总体中每个个体的被抽取不是依据其本身的机会，而是完全决定于调研者的意愿。

其特点为不具有从样本推断总体的功能，但能反映某类群体的特征，是一种快速、简易且节省的数据收集方法。

当研究者对总体具有较好的了解时可以采用此方法，或是总体过于庞大、复杂，采用概率方法有困难时，可以采用非概率抽样来避免概率抽样中容易抽到实际无法实施或“差”的样本，从而避免影响对总体的代表度。

常用的非概率抽样方法有以下四类：方便抽样（Convenience sampling）指根据调查者的方便选取的样本，以无目标、随意的方式进行。

例如：街头拦截访问（看到谁就访问谁）；个别入户项目谁开门就访问谁。

优点：适用于总体中每个个体都是“同质”的，最方便、最省钱；可以在探索性研究中使用，另外还可用于小组座谈会、预测问卷等方面的样本选取工作。

缺点：抽样偏差较大，不适用于要做总体推断的任何民意项目，对描述性或因果性研究最好不要采用方便抽样。

判断抽样（Judgment sampling）指由专家判断而有目的地抽取他认为“有代表性的样本”。

例如：社会学家研究某国家的一般家庭情况时，常以专家判断方法挑选“中型城镇”进行；也有家庭研究专家选取某类家庭进行研究，如选三口之家（子女正在上学的）；在探索性研究中，如抽取深度访问的样本时，可以使用这种方法。

优点：适用于总体的构成单位极不相同而样本数很小，同时设计调查者对总体的有关特征具有相当的了解（明白研究的具体指向）的情况下，适合特殊类型的研究（如产品口味测试等）；操作成本低，方便快捷，在商业性调研中较多用。

缺点：该类抽样结果受研究人员的倾向性影响大，一旦主观判断偏差，则根易引起抽样偏差；不能直接对研究总体进行推断。

配额抽样（Quota sampling）指先将总体元素按某些控制的指标或特性分类，然后按方便抽样或判断抽样选取样本元素。

Sampling methods

SAMPLING METHODGenerally, our company’s sampling method for inspection is: MIL-STD-105E, SINGLE NORMAL LEVEL Ⅱ, AQL isCRITICAL=0, MAJOR=1.5, MINOR=4.0FOR data measurement & testing adopted during inspection, normally, the sampling method shall be SPECIAL 1(S-1).SAMPLING QTY OF CARTON AND SAMPLE SIZEA)Normally, the SAMPLING QTY OF CARTON=√TOTAL CTNS ，then round it. After calculating, we shall double check whether the result is adequate for sampling size: for example---the lot qty was 1600 pcs, 8 pcs were packed into each ctn., the sample size should be 125 pcs, and the sampling cartons should be√1600÷8 =14 ctns, but this result was not correct, because the sample size would be 14 cartons×8 pieces= 112 pieces, which was less than 125 pieces as required, so we should recalculate it, the correct sampling cartons should be 125÷8=16 cartons.B)If the lot size of inspected qty is larger than 35000 pcs or 151 pcs, weshould take more attention to the variation of the sample size. For example, if the lot size is 35001 pcs, as per the AQL table, the sample size shall be 500 pcs, but the sample size between major and minor is deferent, for major it is 500pcs, but for minor it is 315pcs due to the shifting according to the direction of the arrow, that means for the first315 samples, we shall check and count both the major and minor defect, but for the rest samples(500－315=185 pcs), we should only check and count major defect.An important factor for sampling is “randomly” instead of “evenly”or “optionally”.Example 1: ---when you select cartons for inspection, you can try deferent methods instead of keeping only one method:1) Select one raw or layer of the stacked cartons. (refer to figure 2)2) select cartons like stairs. (refer to figure 1)3) select cartons as interval. (refer to figure 3)4) select cartons dispersedly. (refer to figure 4)5) select carton with concentrated method. (refer to figure 5)Figure 3Example 2: --- there were 10 selected cartons with 24 pieces each carton, and the sample size was 125 pieces, normally, we would draw 12 pieces from first 9 cartons, then draw the remains (17 pieces) from the last selected carton, while sometimes, you could draw samples as the following method: 4 pieces in the first carton, 8 in the second, 16 in the third,24 in the forth, then circulate once, then 11 in the ninth, then finally 10 in the tenth.总的来说，我们公司的检验抽样方法是：MIL-STD-105E, SINGLE NORMAL LEVEL Ⅱ, AQL isCRITICAL=0, MAJOR=1.5, MINOR=4.0对于在验货时要进行的数据测量和测试项目，我们通常采用SPECIAL 1(S-1) 的抽样方法。

METHOD FOR IDENTIFYING TERM IMPORTANCE TO A SAMPL

专利名称：METHOD FOR IDENTIFYING TERMIMPORTANCE TO A SAMPLE TEXT USINGREFERENCE TEXT发明人：MAYFIELD, James, C.,MCNAMEE, J., Paul申请号：US2002006036申请日：20020226公开号：WO02/069203P1公开日：20020906专利内容由知识产权出版社提供摘要：A method and apparatus for identifying important terms in a sample text. A frequency of occurrence of terms in the sample text (sample frequency) is compared to a frequency of occurrence of those terms in a reference text (reference frequency). Terms occurring with higher frequency in the sample text than in the reference text are considered important to the sample text. A difference between the respective sample and reference frequencies of a term may be used to determine an importance score. Terms can be ranked and/or added to an affinity set as a function of importance score or rank. When there are insufficient terms for determining a sample frequency, those terms may be used in a search query to identify documents for use as sample text to determine sample frequencies. The important terms may be used for document summarization, query refinement, cross-language translation, and cross-language query expansion.申请人：MAYFIELD, James, C.,MCNAMEE, J., Paul地址：Applied Physics Laboratory 11100 Johns Hopkins Road Laurel, MD 20723-6099 US,9305 Warren Street Silver Spring, MD 20901-1242 US,7969 Brightmeadow Court Ellicott City, MD 21043 US国籍：US,US,US代理机构：ROCA, Benjamin, Y.更多信息请下载全文后查看。

sampling based method

sampling based method
"Sampling-based method" 是一种基于抽样的方法，通常用于从大规模数据集中选择有代表性的样本进行分析和处理。

这种方法的核心思想是通过从数据集中抽取一部分样本，而不是处理整个数据集，来减少计算和时间的复杂性。

通过选择合适的抽样方法，可以在保持数据集的基本特征和统计规律的前提下，有效地利用有限的计算资源和时间。

抽样方法可以根据不同的需求和应用场景进行选择。

一些常见的抽样方法包括简单随机抽样、分层抽样、系统抽样等。

简单随机抽样是从数据集中随机选择样本，每个样本被选中的概率相等。

分层抽样是将数据集按照某些特征或属性进行分层，然后从每个层中进行抽样。

系统抽样是按照一定的规律或间隔从数据集中选择样本。

抽样-based method 在数据分析、机器学习、统计推断等领域中有广泛的应用。

例如，在机器学习中，可以使用抽样方法对大规模数据集进行训练和测试，以减少计算负担和提高效率。

在统计推断中，可以通过抽样来估计总体参数或检验假设。

需要注意的是，抽样-based method 虽然可以减少计算负担，但在使用时需要考虑抽样误差和样本的代表性。

合理的抽样方法和样本大小的选择可以提高分析结果的准确性和可靠性。

重要性采样在大规模数据处理中的应用

重要性采样在大规模数据处理中的应用重要性采样（Importance Sampling）是一种用于估计分布特性的统计方法，广泛应用于大规模数据处理中。

它通过利用已知采样分布来估计目标分布，从而减少采样成本，并提高计算效率。

在大规模数据处理中，重要性采样被广泛应用于概率模型推断、参数估计、机器学习等领域，发挥着重要的作用。

重要性采样的基本思想是，在已知分布下生成样本，并将其作为目标分布的估计。

在大规模数据处理中，由于数据量庞大，直接对目标分布进行采样和计算是非常耗时的。

通过使用重要性采样，我们可以利用已知分布生成样本，以较低的代价估计目标分布的特性。

在概率模型推断中，重要性采样被用于估计概率模型的边缘分布、后验分布等。

通过生成从先验分布中抽取的样本，并为每个样本分配一个重要性权重，我们可以估计后验分布的期望，从而得到概率模型的边缘分布和后验分布的统计特性。

这对于理解概率模型的行为、进行模型选择和比较等具有重要意义。

在参数估计中，重要性采样用于估计模型的参数。

通常情况下，我们可以从已知的简单分布（例如高斯分布）中采样样本，并根据每个样本的重要性权重来估计模型的参数。

这样做可以减少计算成本，并提高参数估计的准确性。

当处理大规模数据时，重要性采样能够更有效地估计参数，从而提高模型的精度和效率。

在机器学习中，重要性采样可应用于分布拟合、模型评估和选择等任务。

通过利用已有数据集的采样分布，我们可以生成新的样本，扩充数据集的规模。

这对于训练更准确的机器学习模型非常有帮助。

此外，重要性采样还可以用于计算模型的评价指标，例如交叉验证中的似然估计（likelihood estimation）。

通过利用重要性采样，我们可以更准确地估计模型的性能，并选择最佳的模型。

除了上述应用之外，重要性采样还被广泛应用于金融风险评估、粒子滤波等领域。

在金融风险评估中，通过估计风险分布的统计特性，我们可以更准确地评估金融市场的风险，并制定相应的风险管理策略。

社会调查方法chapter3 sampling

﹠问题：为什么产品在经历了一个高销售阶段后会停滞不前？
三、决定抽样方案
选择恰当的抽样方法，确定抽样的精确性、把握性及样本规模.
四、实际抽取样本
即在前进几个步骤的基础上，严格按照所选定的抽样方法，从抽样框中抽取一个个抽样单位，构成调查样本。
五、评估样本质量
所谓样本评估，就是对样本的质量、代表性、偏差等进行初步的检验和衡量，其目的是防止由于前面步骤中的失误而使样本偏差太大，进而导致整个调查的失误。
例：重庆城市管理职业学院在校学生对食堂满意度的调查
3.抽样（Sampling）是一种选择调查对象的程序与方法，即从总体中选取一部分代表的过程，也即从总体中按一定方式选择或抽取样本的过程。
4.抽样单位(Sampling Unit) 一次直接的抽样所使用的基本单位。抽样单位和构成总体的元素有时相同，有时不同。
★分层比例（1）按比例分层（2）不按比例分层如：某厂有工人600人，按照性别分层有男工500人，女工100
5.抽样框（Sampling Frame）也称抽样范围，指抽取样本时总体所有抽样单位的名单。
第四章抽样
例：重庆城市管理职业学院在校学生对食堂满意度的调查
6.参数值(Parameter) 也称总体值，是关于总体中某一变量的综合描述。
7.统计值（Statistic）也称样本值，是关于样本中某一变量的综合描述。
四、样本规模与抽样误差
任务一认识抽样
一、抽样的概念和作用
例：重庆城市管理职业学院在校学生对食堂满意度的调查
（一）抽样的概念及相关术语
1、总体（Population）（在社会调查中用N表示）通常与构成的元素共同定义，总体是构成它的所有元素的集合，而元素则是构成总体的基本单位。

如何理解重要性采样（importancesampling）

如何理解重要性采样（importancesampling）重要性采样是非常有意思的一个方法。

我们首先需要明确，这个方法是基于采样的，也就是基于所谓的蒙特卡洛法(Monte Carlo)。

蒙特卡洛法，本身是一个利用随机采样对一个目标函数做近似。

例如求一个稀奇古怪的形状的面积，如果我们没有一个解析的表达方法，那么怎么做呢？蒙特卡洛法告诉我们，你只要均匀的在一个包裹了这个形状的范围内随机撒点，并统计点在图形内的个数，那么当你撒的点很多的时候，面积可以近似为=(在图形内的点的个数/总的点个数)，当你撒的点足够多的时候，这个值就是面积。

这里假设我们总有办法（至少要比找解析的面积公式简单）求出一个点是否在图形内。

另一个例子，如果你要求一个稀奇古怪的积分，没有解析办法怎么办？蒙特卡洛法告诉你，同样，随机撒点，你一定可以知道f(xi)的值，那么这个积分的解可以表示为=(b-a)/点的个数*sigma[f(xi)]，其中b,a 为积分的上下限。

好了，知道了蒙特卡洛法，下面来说重要性采样的前提一些内容。

很多问题里，我们需要知道一个随机变量的期望E(X)，更多时候，我们甚至需要知道关于X的某一个函数f(X)的期望E[f(X)]。

问题来了，如果这个X的概率分布超级特么的复杂，你准备怎么做呢？积分么？逐点求和么？听上去挺不现实的。

这时蒙特卡洛法跑出来告诉你，来来来，咱只要按照你这个概率分布，随机的取一些样本点，再sigma(p(xi)*f(xi))不就可以近似这个期望了么。

但问题又来了，你怎么”按照这个概率分布“去撒点呢？经典蒙特卡洛法是这么做的，首先把这个概率分布写成累计概率分布的形式，就是从pdf写成cdf，然后在[0,1]上均匀取随机数(因为计算机只能取均匀随机数)，假如我们取到了0.3，那么在cdf上cdf(x0)=0.3的点x0就是我们依据上述概率分布取得的随机点。

举个具体例子吧，例如我想按照标准正态分布N(0,1)取10个随机数，那么我首先在[0,1]上按照均匀分布取10个点0.4505 0.0838 0.2290 0.9133 0.1524 0.8258 0.5383 0.9961 0.0782 0.4427然后，我去找这些值在cdf上对应的x0，如下-0.1243 -1.3798 -0.7422 1.3616 -1.0263 0.9378 0.0963 2.6636 -1.4175 -0.1442那么上述这些点，就是我按照正态分布取得的10个随机数。

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participants at the Cowles Conference on Strategy and Decision Making and the MIT Econometrics Lunch for helpful discussions. All errors are my own.
1
can be also be used to dramatically reduce the number of times a complicated economic model needs to be solved within an estimation procedure. Instead of solving the model N S ` N ` R times, with importance sampling one only needs to solve the model N S ` N times or N S times. Since R can be quite large (e.g. when the number of parameters is around 8 and the function is well behaved, at a minimum R might of parameters), this can lead to very signi¿cant time savings. 500 — and R tends to increase exponentially in the number
A 0 . So is the expectation of any function g xi of the
conditioning variables multiplied by the difference between y and its expectation, i.e. E [ yi E [ f xi > i A xi ] ` gxi ] 0 at A A0 (1)
Method of Simulated Moments (MSM) estimators (MacFadden (1989), Pakes and Pollard (1989)) have great value to applied economists estimating structural models due to their simple and intuitive nature. Regardless of the degree of complication of the econometric model, one only needs the ability to generate simulated data according to that model. Moments of these simulated data can then be matched to moments of the true data in an estimation procedure. The value of the parameters that sets the moments of the simulated data ”closest” to the moments of the actual data is an MSM estimate. Such estimates typically have nice properties such as consistency and asymptotic normality, even for a ¿nite amount of simulation draws. This note addresses a caveat of such procedures that occurs when it is time consuming to solve and generate data from one’s model. Examples include 1) complicated equilibrium problems, e.g. discrete games or complicated auction models, and 2) dynamic programming problems with large state spaces or signi¿cant amounts of heterogeneity. In the above estimation procedure, one usually needs to solve such a model numerous times, typically once for every simulation draw, for every observation, for every parameter vector that is ever evaluated in an optimization procedure. If one has N observations, performs N S simulation draws per observation, and optimization requires R function evaluations, estimation requires solving the model N S ` N ` R times. This can be unwieldy for these complicated problems. We suggest using a change of variables and importance sampling to alleviate or remove this problem. Importance sampling is a technique most noted for its ability to reduce levels of simulation error. We show that importance sampling Dept. of Economics, Boston University and NBER (ackerber@). Thanks to Steve Berry, Ariel Pakes, Whitney Newey, Peter Davis and
Importance Sampling and the Method of Simulated Moments
Daniel A. Ackerberg` This Version: May 16, 2000
Abstract Method of Simulated Moments (MSM) estimators introduced by McFadden (1989) and Pakes and Pollard (1989) are of great use to applied economists. They are relatively easy to use even for estimating very complicated economic models. One simply needs to generate simulated data according to the model and choose parameters that make moments of this simulated data as close as possible to moments of the true data. This paper uses importance sampling techniques to address a signi¿cant computational caveat regarding these MSM estimators – that often one’s economic model is hard to solve. Examples include complicated equilibrium models and dynamic programming problems. We show that importance sampling can reduce the number of times a particular model needs to be solved in an estimation procedure, signi¿cantly decreasing computational burden.
As a result, the value of A , say E A , that sets the sample analog of this moment G N A 1 ; [ yi E [ f xi > i A] ` g xi ] N i
equal to zero or as close as possible to zero is a consistent estimator of A 0 . Under appropriate regularity conditions, one obtains asymptotic normality of E A (Hansen (1982)).1 Simulation enters the picture when the function E [ f xi > i A xi ] is not easily computable. The straightforward way of simulating this expectation is by averaging f xi > i A over a set of N S random draws > i1 > i N S from the distribution of > i , i.e. G E f i A 1 ; f xi > ins A N S ns (2)