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Spatial Statistical Methods for Geography [Pehme köide]

  • Formaat: Paperback / softback, 256 pages, kõrgus x laius: 242x170 mm, kaal: 440 g
  • Ilmumisaeg: 29-Mar-2021
  • Kirjastus: Sage Publications Ltd
  • ISBN-10: 1529707447
  • ISBN-13: 9781529707441
Teised raamatud teemal:
Spatial Statistical Methods for GeographySuurem pilt
  • Formaat: Paperback / softback, 256 pages, kõrgus x laius: 242x170 mm, kaal: 440 g
  • Ilmumisaeg: 29-Mar-2021
  • Kirjastus: Sage Publications Ltd
  • ISBN-10: 1529707447
  • ISBN-13: 9781529707441
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781529707441.html
Märksõnad:

This accessible new textbook offers a straightforward introduction to doing spatial statistics in the context of unique considerations that apply with geographic data. Grounded in real world examples, it shows you how to extend traditional statistical methods for use with spatial data.




This accessible new textbook offers a straightforward introduction to doing spatial statistics. Grounded in real world examples, it shows you how to extend traditional statistical methods for use with spatial data.

The book assumes basic mathematical and statistics knowledge but also provides a handy refresher guide, so that you can develop your understanding and progress confidently. It also:

·       Equips you with the tools to both interpret and apply spatial statistical methods

·       Engages with the unique considerations that apply when working with geographic data

·       Helps you build your knowledge of key spatial statistical techniques, such as methods of geographic cluster detection.



Arvustused

This book provides a lively introduction into spatial statistics. Several test statistics are presented and discussed from a traditional statistical point of departure. I can recommend the book in particular to quantitative geographers interested in spatial statistics. -- Alfred Stein "Rogersons book is a cost-effective, comprehensive, and yet easy-to-understand overview of spatial concepts and techniques for students at the undergraduate and graduate levels." p32





"From the reviewers perspective, this is an excellent technique with which to teach geography statistics for in-class and assignment-based contexts." p32





"This book is important in the field of spatial statistics with a comprehensive discussion of a broad selection of commonly to less commonly employed spatial statistical tests. The detailed by hand and programmed examples that directly address the goals of the book would enable students to repeat the tests with the supplied data and then apply the techniques and thinking to their own data." 34 -- Christopher Hewitt

List of figures
x
List of tables
xii
About the author xiv
Acknowledgements xv
Preface xvi
Online resources xviii
1 Introduction to Spatial Statistical Methods for Geography
1(10)
1.1 Spatial dependence
2(1)
1.2 Spatial patterns
2(2)
1.3 Some motivating problems
4(7)
1.3.1 Perceptions of randomness - visual assessment of maps
4(3)
1.3.2 Distinguishing random coin tosses from a series constructed to appear random
7(1)
1.3.3 Distinguishing a random pattern of points from a pattern of glowworm locations
8(1)
1.3.4 Finding the mean for spatial data
9(2)
2 A Quick Review of Some Key Material from Introductory Statistics
11(12)
2.1 Introduction
11(1)
2.2 Probability and probability distributions
12(5)
2.2.1 Binomial distribution
12(1)
2.2.2 Poisson distribution
13(1)
2.2.3 Normal distribution
14(1)
2.2.4 Exponential distribution
15(2)
2.3 The distribution of sample means
17(1)
2.4 Confidence intervals
17(1)
2.5 Hypothesis testing
18(5)
3 Some Selected Measures for Descriptive Spatial Statistical Analysis
23(34)
3.1 Centers of population
24(8)
3.1.1 Mean center
24(1)
3.1.2 Median center
25(1)
3.1.3 Centers of population for large geographic regions
26(1)
3.1.3.1 The mean center of population as calculated by the US Bureau of the Census
26(1)
3.1.3.2 The azimuthal equidistant projection
27(1)
3.1.3.3 The three-dimensional solution
28(1)
3.1.3.4 The median center for points on a sphere
29(3)
3.2 Measures of dispersion
32(2)
3.2.1 The standard deviational ellipse
33(1)
3.3 Measures of "coastiality"
34(3)
3.3.1 The Hu line
34(1)
3.3.2 The depth of the three-dimensional center of population
35(2)
3.4 Geographic centers
37(6)
3.4.1 Geographic center for two-dimensional polygons
38(1)
3.4.2 Geographic centers for the three-dimensional case
39(1)
3.4.3 Geographic center of the continental United States
40(1)
3.4.4 Geographic centers of continents
40(1)
3.4.4.1 Center of Asia
41(1)
3.4.4.2 Comments on centers of other selected continents
42(1)
3.5 Measures of inequality
43(14)
3.5.1 Measures of inequality in physical geography and other fields
48(6)
3.5.2 Surface metrology
54(3)
4 Statistical Inference and Spatial Patterns
57(18)
4.1 Types of data
57(1)
4.2 Characteristics of randomness
58(1)
4.3 Classes of questions regarding spatial patterns
58(1)
4.3.1 Global or general tests
58(1)
4.3.2 Focused or local tests
58(1)
4.3.3 Tests for the detection of clustering -- scan tests
59(1)
4.4 Circular study areas
59(5)
4.4.1 Simulation approach
61(2)
4.4.2 An exact approach
63(1)
4.5 Square study areas
64(4)
4.5.1 Simulation
65(3)
4.6 Global tests: history and perspective
68(7)
4.6.1 Nearest neighbor statistic
68(7)
5 GLOBAL TESTS
75(33)
5.1 Quadrat tests
75(7)
5.1.1 Generalization to chi-square goodness-of-fit tests
77(1)
5.1.2 Minimal expectations
78(1)
5.1.3 Scale
78(1)
5.1.4 Multiple testing of different grid sizes
79(1)
5.1.5 Statistical power
79(2)
5.1.6 A further word on expectations
81(1)
5.1.7 Further limitations
82(1)
5.2 Moran's I
82(6)
5.2.1 Hypothesis testing
85(3)
5.3 Geary's C
88(1)
5.3.1 Comparison of C and I
88(1)
5.4 Tango's statistic
89(1)
5.5 A spatial version of the chi-square statistic
90(3)
5.6 Significance of Tango's statistic and the spatial chi-square statistic
93(7)
5.6.1 COVID-19 cases in a region of New York State
99(1)
5.7 Global statistics for case-control data
100(8)
5.7.1 A quadrat test for case-control data
102(6)
6 Local Tests
108(26)
6.1 Introduction
108(1)
6.2 Local quadrat test
109(1)
6.3 Stone's test
110(1)
6.4 Kolmogorov--Smirnov test
111(1)
6.5 Score statistic
112(2)
6.6 Modified local score statistic
114(1)
6.7 Getis--Ord statistic
114(1)
6.8 Local Moran statistic
115(1)
6.9 Illustrations
116(4)
6.9.1 Stone's test
117(1)
6.9.2 Kolmogorov--Smirnov test
117(1)
6.9.3 Score statistic
117(1)
6.9.4 Local version of the spatial chi-square statistic
118(1)
6.9.5 Getis--Ord Gi statistic
118(1)
6.9.6 Local Moran's I
119(1)
6.10 Local statistics for case-control data
120(4)
6.10.1 Maximum chi-square test
123(1)
6.11 Other issues with local statistics
124(10)
6.11.1 Weights and multiple definitions of scale
124(5)
6.11.2 Global spatial autocorrelation
129(5)
7 Tests for the Detection of Clustering: Scan Tests
134(18)
7.1 Introduction: multiple testing
134(1)
7.2 Basic aspatial scan test -- maximum of aspatial z-scores (M-test)
135(2)
7.3 Kulldorff's spatial scan statistic
137(4)
7.3.1 Likelihood ratio tests
137(4)
7.4 A Gaussian scan statistic
141(5)
7.4.1 Some spatial applications
145(1)
7.5 A simple Gaussian scan statistic
146(3)
7.6 Rectangular scan statistic
149(3)
8 Spatial Means, Spatial Models, and Spatial Regression
152(33)
8.1 Spatial means
152(5)
8.2 Spatial models
157(3)
8.3 Estimation of ρ
160(4)
8.3.1 Estimation of ρ when μ is known
160(2)
8.3.2 What happens when μ, σ, and ρ are all unknown?
162(2)
8.4 Type I and Type II errors, p-values, and critical values with spatial data
164(17)
8.4.1 Confidence intervals, Type I errors, and adjusted critical values and p-values when observations are spatially dependent
166(2)
8.4.2 Type II errors
168(5)
8.4.3 m × m systems
173(2)
8.4.4 Two-sample tests
175(2)
8.4.5 Illustrations
177(4)
8.5 Spatial regression
181(4)
Epilogue
185(2)
Appendix A Some Preparatory Tools
187(38)
A.1 A calculus primer: derivatives and integrals
187(5)
A.1.1 Integrals as areas under curves
188(2)
A.1.2 Areas under probability density functions as probabilities
190(1)
A.1.3 Derivatives
190(2)
A.2 Matrix algebra: a short and gentle introduction
192(11)
A.2.1 Matrix multiplication
193(1)
A.2.2 Other terminology and properties
193(2)
A.2.3 Matrix form of regression
195(2)
A.2.4 Extensions and generalizations of ordinary least squares regression
197(1)
A.2.4.1 Weighted least squares
197(1)
A.2.4.2 Generalized least squares
198(1)
A.2.4.3 Ridge regression
198(2)
A.2.4.4 Omitted variable bias
200(1)
A.2.4.5 Outliers and the hat matrix
201(2)
A.3 Review and extension of some probability theory
203(4)
A.3.1 Expected values
204(2)
A.3.2 Variance of a random variable
206(1)
A.4 Parameter estimation
207(5)
A.4.1 Median estimator
208(1)
A.4.2 Method of moments
208(1)
A.4.3 Maximum likelihood
209(3)
A.5 Simulation of variates from probability distributions
212(1)
A.6 Practice with distributions
213(12)
A.6.1 An illustration with a somewhat contrived distribution
213(4)
A.6.2 The intervening opportunities model
217(3)
A.6.3 Pareto distribution
220(5)
Appendix B Equations for Azimuthal equidistant projection
225(1)
References 226(5)
Index 231
Peter A. Rogerson is SUNY (State University of New York) Distinguished Professor in the Department of Geography at the University at Buffalo, Buffalo, New York, USA. He also holds an adjunct appointment in the Department of Biostatistics.