应用地质统计学 (国外大学教授主讲)

IQR
Q Q
3
1
CS
3 1 n xi n i 1

2
CV
Bivariate
Scatterplots
p
Yin
Correlation
1 n
p
p
y x
n i 1 i x i y
X in
Linear Regression
coordinates
{Z(s): s D} Geostatistics: Z random; D fixed, infinite, continuous Lattice Models: Z random; D fixed, finite, (ir)regular grid Point Patterns: Z 1; D random, finite
Configuration = The physical distribution in space and
spatial character of elements.
Isolation, placement, adjacency ** some metrics do both **
Types of Metics
Lags
Variograms: How do we estimate them?
Binning Lags
Variograms: How do we estimate them?
1
1
2
2 3 4
4
3
Let’s review:
VECTOR
1
2
3 OR
Geostatistics Univariate Bivariate Spatial Description -
p
Yin
X in
p
2
2
10 15
RASTER
-Data Postings => symbol maps -Contour Maps •Moving Windows => “heteroscedasticity” •Spatial Continuity h-scatterplots
3
12
OR: as |h| points drift away from x=y
Isotropy
Variograms: What are their features?
Anisotropy
Variograms: What are their features?
Anisotropy
Variograms: What are their features?
Definitions
Variograms: What are they?
Covariance C (h) cov( Z (s), Z (s h)) Autocorrelation (h) C (h) / C (0) Variogram 2 (h) var( Z (s) Z (s h))



Double log fractal dimension (DLFD) Mean patch fractal (MPFD) Area-weighted mean patch fractal dimension (AWMPFD)
Contagion, Interspersion and Juxtaposition
Shape Metrics
perimeter-area relationships
Shape Index (SHAPE) -- complexity of patch compared to standard shape
vector uses circular; raster uses square Mean Shape Index (MSI) = perimeter-to-area ratio Area-Weighted Mean Shape Index (AWMSI) Landscape Shape Index (LSI)

x
y
y ax b
slope constant
a
b y a x
p
y x
Autocorrelation
Values at locations that are near to each other are more similar than values at locations that are farther apart.
Spatial Description
Spatial lag = h = (0,1) = same x, y+1
h=(0,0)
h=(0,3)
h=(0,5) * (0,0)
tj
hij=tj-ti * Xi,Yi
ti
correlation coefficient
(i.e the correlogram, relationship of p with h
Fractal Dimension (D), or (FRACT)
log P = 1/2D*log A; P = perimeter, A = area P = sq.rt. A raised to D, and D = 1 (a line) as polygons move to complexity P = A, and D -> 2 A few fractal metrics
1 n 2n i 1
x y
i i
2
OR: half the average sum difference between the x and y pair of the h-scatterplot
ቤተ መጻሕፍቲ ባይዱ
OR: for a h(0,0) all points fall on a line x=y
Anisotropy
Variograms: What are their features?
Structured Process in Geostatistics
Represent the Represent the Data Data Explore the Data Explore the Data Fit a Model Fit a Model Perform Perform Diagnostics Diagnostics Compare the Compare the Models Models
Applied Geostatistics
Miles Logsdon mlog@u.washington.edu
Mimi D’Iorio mimid@u.washington.edu
•"An Introduction to Applied Geostatistics" by Edward H. Isaaks and R. Mohan Srivastava, Oxford University Press, 1989.
Area Metrics Patch Density, Size and Variability Edge Metrics Shape Metrics Core Area Metrics Nearest-Neighbor Metrics Diversity Metrics Contagion and Interspersion Metrics
•Spatial Description
Univariate
•One Variable •Frequency (table) •Histogram (graph) •Do the same thing (i.e count of observations in intervals or classes •Cumulative Frequency (total “below” cutoffs)
•Correlogram = p(h) = the relationship of the correlation coefficient of an h-scatterplot and h (the spatial lag) •Covariance = C(h) = the relationship of the coefficient of variation of an h-scatterplot and h •Semivariogram = variogram = (h) = moment of inertia moment of inertia =
Introduction to Geostatistics
D
Z(s)
• D is the spatial domain or area of
interest
• s contains the spatial coordinates • Z is a value located at the spatial
- Data Postings = symbol maps (if only 2 classes = indicator map - Contour Maps - Moving Windows => “heteroscedasticity” (values in some region are more variable than in others) - Spatial Continuity (h-scatterplots * Xj,Yj
Summary of a histogram
Measurements of location (center of distribution
mean (m µ x ) median mode

n 2 i 1
x
i 1
n
i
Measurements of spread (variability)
When first proposed (O’Neill 1988) proved incorrect, Li & Reynolds (1993) alternative Based upon the product of two (2) probabilities
variance standard deviation interquartile range
1 / n xi
2
n
2
st . d . Measurements of shape (symmetry
& length
coefficient of skewness coefficient of variation
•"Spatial Data Analysis: Theroy and Practice" by Robert Haining, Cambridge University Press, 1993. •"Statistics for Spatial data" by Noel a. c. Cressie, Wiley & Sons, Inc. 1991.
GeoStatistics
-A way of describing the spatial continuity as an essential feature of natural phenomena. - The science of uncertainty which attempts to model order in disorder. - Recognized to have emerged in the early 1980’s as a hybrid of mathematics, statistics, and mining engineering. - Now extended to spatial pattern description •Univariate •Bivariate
Physiognomy / Pattern / structure
Composition = The presence and amount of each
element type without spatially explicit measures.
Proportion, richness, evenness, diversity
5
1
11
4 Spatial Lag = h = distance
Lag bins
1 2 3 4
Values at locations that are near to each other are more similar than values at locations that are farther apart. = Autocorrelation