Spatial statistical methods for geography:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Los Angeles
SAGE
2021
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvii, 234 Seiten Illustrationen, Diagramme, Karten (schwarz-weiß) |
| ISBN: | 9781529707441 9781529707458 |
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| 245 | 1 | 0 | |a Spatial statistical methods for geography |c Peter A. Rogerson |
| 264 | 1 | |a Los Angeles |b SAGE |c 2021 | |
| 300 | |a xvii, 234 Seiten |b Illustrationen, Diagramme, Karten (schwarz-weiß) | ||
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Datensatz im Suchindex
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| adam_text | Contents List of figures List of tables About the author Acknowledgements Preface Online resources 1 INTRODUCTION TO SPATIAL STATISTICAL METHODS FOR GEOGRAPHY 1.1 1.2 1.3 2 Spatial dependence Spatial patterns Some motivating problems 1.3.1 Perceptions of randomness - visual assessment of maps 1.3.2 Distinguishing random coin tosses from a series constructed to appear random 1.3.3 Distinguishing a random pattern of points from a pattern of glowworm locations 1.3.4 Finding the mean for spatial data A QUICK REVIEW OF SOME KEY MATERIAL FROM INTRODUCTORY STATISTICS 2.1 2.2 3 X xii xiv xv xvi xviii 1 2 2 4 4 7 8 9 11 Introduction Probability and probability distributions 2.2.1 Binomial distribution 2.2.2 Poisson distribution 2.2.3 Normal distribution 2.2.4 Exponential distribution 2.3 The distribution of sample means 2.4 Confidence intervals 2.5 Hypothesis testing 11 12 12 13 14 15 17 17 18 SOME SELECTED MEASURES FOR DESCRIPTIVE SPATIAL STATISTICAL ANALYSIS 23 3.1 Centers of population 3.1.1 Mean center 3.1.2 Median center 24 24 25
Contents VI 3.1.3 3.2 3.3 3.4 3.5 4 5 Centers of population for large geographic regions 3.1.3.1 The mean center of population as calculated by the US Bureau of the Census 3.1.3.2 The azimuthal equidistant projection 3.1.3.3 The three-dimensional solution 3.1.3.4 The median center for points on a sphere Measures of dispersion 26 3.2.1 33 The standard deviational ellipse Measures of coastiality 3.3.1 The Hu line 3.3.2 The depth of the three-dimensional center of population Geographic centers 3.4.1 Geographic center for two-dimensional polygons 3.4.2 Geographic centers for the three-dimensional case 3.4.3 Geographic center of the continental United States 3.4.4 Geographic centers of continents 3.4.4.1 Center of Asia 3.4.4.2 Comments on centers of other selected continents Measures of inequality 3.5.1 Measures of inequality in physical geography and other fields 3.5.2 Surface metrology 26 27 28 29 32 34 34 35 37 38 39 40 40 41 42 43 48 54 STATISTICAL INFERENCE AND SPATIAL PATTERNS 57 4.1 Types of data 4.2 Characteristics of randomness 4.3 Classes of questions regarding spatial patterns 4.3.1 Global or general tests 4.3.2 Focused or local tests 4.3.3 Tests for the detection of clustering - scantests 4.4 Circular study areas 4.4.1 Simulation approach 4.4.2 An exact approach 4.5 Square study areas 4.5.1 Simulation 4.6 Global tests: history and perspective 4.6.1 Nearest neighbor statistic 57 58 58 58 58 59 59 61 63 64 65 68 68 GLOBAL TESTS 75 5.1 75 77 78 Quadrat tests 5.1.1 Generalization to chi-square goodness-of-fittests 5.1.2 Minimal expectations
Contents 5.2 5.3 5.4 5.5 5.6 5.7 6 7 5.1.3 Scale 5.1.4 Multiple testing of different grid sizes 5.1.5 Statistical power 5.1.6 A further word on expectations 5.1.7 Further limitations Moran s I 5.2.1 Hypothesis testing Geary s C 5.3.1 Comparison of C and/ Tango s statistic A spatial version of the chi-square statistic Significance of Tango s statistic andthe spatial chi-square statistic 5.6.1 COVID-19 cases in a regionof New York State Global statistics for case-control data 5.7.1 A quadrat test for case-control data vH 78 79 79 81 82 82 85 88 88 89 90 93 99 100 102 LOCAL TESTS 108 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 Introduction Local quadrat test Stone s test Kolmogorov-Smirnov test Score statistic Modified local score statistic Getis-Ord statistic Local Moran statistic Illustrations 6.9.1 Stone s test 6.9.2 Kolmogorov-Smirnov test 6.9.3 Score statistic 6.9.4 Local version of the spatial chi-square statistic 6.9.5 Getis-Ord G, statistic 6.9.6 Local Moran s / 6.10 Local statistics for case-control data 6.10.1 Maximum chi-square test 6.11 Other issues with local statistics 6.11.1 Weights and multiple definitions of scale 6.11.2 Global spatial autocorrelation 108 109 110 111 112 114 114 115 116 117 117 117 118 118 119 120 123 124 124 129 TESTS FOR THE DETECTION OF CLUSTERING: SCAN TESTS 134 7.1 7.2 134 135 Introduction: multiple testing Basic aspatial scan test - maximumof aspatial z-scores (M-test)
Contents VIII 7.3 7.4 7.5 7.6 8 Kulldorff s spatial scan statistic 7.3.1 Likelihood ratio tests A Gaussian scan statistic 7.4.1 Some spatial applications A simple Gaussian scan statistic Rectangular scan statistic SPATIAL MEANS, SPATIAL MODELS, AND SPATIAL REGRESSION 8.1 8.2 8.3 8.4 8.5 Spatial means Spatial models Estimation of p 8.3.1 Estimation of p when μ is known 8.3.2 What happens when μ, σ, and p are all unknown? Type I and Type II errors, p-values, and critical values with spatial data 8.4.1 Confidence intervals, Type I errors, and adjusted critical values and p-values when observations are spatially dependent 8.4.2 Type II errors 8.4.3 mxm systems 8.4.4 Two-sample tests 8.4.5 Illustrations Spatial regression Epilogue Appendix A: some preparatory tools A.l A calculus primer: derivatives and integrals A. 1.1 Integrals as areas under curves A. 1.2 Areas under probability density functions as probabilities A. 1.3 Derivatives A. 2 Matrix algebra: a short and gentle introduction A.2.1 Matrix multiplication A.2.2 Other terminology and properties A.2.3 Matrix form of regression A.2.4 Extensions and generalizations of ordinary least squares regression A.2.4.1 Weighted least squares A.2.4.2 Generalized least squares A.2.4.3 Ridge regression A.2.4.4 Omitted variable bias A.2.4.5 Outliers and the hat matrix 137 137 141 145 146 149 152 152 157 160 160 162 164 166 168 173 175 177 181 185 187 187 188 190 190 192 193 193 195 197 197 198 198 200 201
Contents А.З Review and extension of some probability theory A.3.1 Expected values A.3.2 Variance of a random variable A.4 Parameter estimation A.4.1 Median estimator A.4.2 Method of moments A.4.3 Maximum likelihood A.5 Simulation of variates from probability distributions A.6 Practice with distributions A.6.1 An illustration with a somewhat contrived distribution A.6.2 The intervening opportunities model A.6.3 Pareto distribution Appendix B: Equations for Azimuthal equidistant projection References Index IX 203 204 206 207 208 208 209 212 213 213 217 220 225 226 231
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| adam_txt |
Contents List of figures List of tables About the author Acknowledgements Preface Online resources 1 INTRODUCTION TO SPATIAL STATISTICAL METHODS FOR GEOGRAPHY 1.1 1.2 1.3 2 Spatial dependence Spatial patterns Some motivating problems 1.3.1 Perceptions of randomness - visual assessment of maps 1.3.2 Distinguishing random coin tosses from a series constructed to appear random 1.3.3 Distinguishing a random pattern of points from a pattern of glowworm locations 1.3.4 Finding the mean for spatial data A QUICK REVIEW OF SOME KEY MATERIAL FROM INTRODUCTORY STATISTICS 2.1 2.2 3 X xii xiv xv xvi xviii 1 2 2 4 4 7 8 9 11 Introduction Probability and probability distributions 2.2.1 Binomial distribution 2.2.2 Poisson distribution 2.2.3 Normal distribution 2.2.4 Exponential distribution 2.3 The distribution of sample means 2.4 Confidence intervals 2.5 Hypothesis testing 11 12 12 13 14 15 17 17 18 SOME SELECTED MEASURES FOR DESCRIPTIVE SPATIAL STATISTICAL ANALYSIS 23 3.1 Centers of population 3.1.1 Mean center 3.1.2 Median center 24 24 25
Contents VI 3.1.3 3.2 3.3 3.4 3.5 4 5 Centers of population for large geographic regions 3.1.3.1 The mean center of population as calculated by the US Bureau of the Census 3.1.3.2 The azimuthal equidistant projection 3.1.3.3 The three-dimensional solution 3.1.3.4 The median center for points on a sphere Measures of dispersion 26 3.2.1 33 The standard deviational ellipse Measures of "coastiality" 3.3.1 The Hu line 3.3.2 The depth of the three-dimensional center of population Geographic centers 3.4.1 Geographic center for two-dimensional polygons 3.4.2 Geographic centers for the three-dimensional case 3.4.3 Geographic center of the continental United States 3.4.4 Geographic centers of continents 3.4.4.1 Center of Asia 3.4.4.2 Comments on centers of other selected continents Measures of inequality 3.5.1 Measures of inequality in physical geography and other fields 3.5.2 Surface metrology 26 27 28 29 32 34 34 35 37 38 39 40 40 41 42 43 48 54 STATISTICAL INFERENCE AND SPATIAL PATTERNS 57 4.1 Types of data 4.2 Characteristics of randomness 4.3 Classes of questions regarding spatial patterns 4.3.1 Global or general tests 4.3.2 Focused or local tests 4.3.3 Tests for the detection of clustering - scantests 4.4 Circular study areas 4.4.1 Simulation approach 4.4.2 An exact approach 4.5 Square study areas 4.5.1 Simulation 4.6 Global tests: history and perspective 4.6.1 Nearest neighbor statistic 57 58 58 58 58 59 59 61 63 64 65 68 68 GLOBAL TESTS 75 5.1 75 77 78 Quadrat tests 5.1.1 Generalization to chi-square goodness-of-fittests 5.1.2 Minimal expectations
Contents 5.2 5.3 5.4 5.5 5.6 5.7 6 7 5.1.3 Scale 5.1.4 Multiple testing of different grid sizes 5.1.5 Statistical power 5.1.6 A further word on expectations 5.1.7 Further limitations Moran's I 5.2.1 Hypothesis testing Geary's C 5.3.1 Comparison of C and/ Tango's statistic A spatial version of the chi-square statistic Significance of Tango's statistic andthe spatial chi-square statistic 5.6.1 COVID-19 cases in a regionof New York State Global statistics for case-control data 5.7.1 A quadrat test for case-control data vH 78 79 79 81 82 82 85 88 88 89 90 93 99 100 102 LOCAL TESTS 108 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 Introduction Local quadrat test Stone's test Kolmogorov-Smirnov test Score statistic Modified local score statistic Getis-Ord statistic Local Moran statistic Illustrations 6.9.1 Stone's test 6.9.2 Kolmogorov-Smirnov test 6.9.3 Score statistic 6.9.4 Local version of the spatial chi-square statistic 6.9.5 Getis-Ord G, statistic 6.9.6 Local Moran's / 6.10 Local statistics for case-control data 6.10.1 Maximum chi-square test 6.11 Other issues with local statistics 6.11.1 Weights and multiple definitions of scale 6.11.2 Global spatial autocorrelation 108 109 110 111 112 114 114 115 116 117 117 117 118 118 119 120 123 124 124 129 TESTS FOR THE DETECTION OF CLUSTERING: SCAN TESTS 134 7.1 7.2 134 135 Introduction: multiple testing Basic aspatial scan test - maximumof aspatial z-scores (M-test)
Contents VIII 7.3 7.4 7.5 7.6 8 Kulldorff's spatial scan statistic 7.3.1 Likelihood ratio tests A Gaussian scan statistic 7.4.1 Some spatial applications A simple Gaussian scan statistic Rectangular scan statistic SPATIAL MEANS, SPATIAL MODELS, AND SPATIAL REGRESSION 8.1 8.2 8.3 8.4 8.5 Spatial means Spatial models Estimation of p 8.3.1 Estimation of p when μ is known 8.3.2 What happens when μ, σ, and p are all unknown? Type I and Type II errors, p-values, and critical values with spatial data 8.4.1 Confidence intervals, Type I errors, and adjusted critical values and p-values when observations are spatially dependent 8.4.2 Type II errors 8.4.3 mxm systems 8.4.4 Two-sample tests 8.4.5 Illustrations Spatial regression Epilogue Appendix A: some preparatory tools A.l A calculus primer: derivatives and integrals A. 1.1 Integrals as areas under curves A. 1.2 Areas under probability density functions as probabilities A. 1.3 Derivatives A. 2 Matrix algebra: a short and gentle introduction A.2.1 Matrix multiplication A.2.2 Other terminology and properties A.2.3 Matrix form of regression A.2.4 Extensions and generalizations of ordinary least squares regression A.2.4.1 Weighted least squares A.2.4.2 Generalized least squares A.2.4.3 Ridge regression A.2.4.4 Omitted variable bias A.2.4.5 Outliers and the hat matrix 137 137 141 145 146 149 152 152 157 160 160 162 164 166 168 173 175 177 181 185 187 187 188 190 190 192 193 193 195 197 197 198 198 200 201
Contents А.З Review and extension of some probability theory A.3.1 Expected values A.3.2 Variance of a random variable A.4 Parameter estimation A.4.1 Median estimator A.4.2 Method of moments A.4.3 Maximum likelihood A.5 Simulation of variates from probability distributions A.6 Practice with distributions A.6.1 An illustration with a somewhat contrived distribution A.6.2 The intervening opportunities model A.6.3 Pareto distribution Appendix B: Equations for Azimuthal equidistant projection References Index IX 203 204 206 207 208 208 209 212 213 213 217 220 225 226 231 |
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| spelling | Rogerson, Peter 20. Jht. Verfasser (DE-588)1089205589 aut Spatial statistical methods for geography Peter A. Rogerson Los Angeles SAGE 2021 xvii, 234 Seiten Illustrationen, Diagramme, Karten (schwarz-weiß) txt rdacontent n rdamedia nc rdacarrier Methode (DE-588)4038971-6 gnd rswk-swf Geografie (DE-588)4020216-1 gnd rswk-swf Räumliche Statistik (DE-588)4386767-4 gnd rswk-swf Spatial analysis (Statistics) Geography / Statistical methods Geografie (DE-588)4020216-1 s Räumliche Statistik (DE-588)4386767-4 s Methode (DE-588)4038971-6 s DE-604 Erscheint auch als Online-Ausgabe 9781529756333 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032646728&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rogerson, Peter 20. Jht Spatial statistical methods for geography Methode (DE-588)4038971-6 gnd Geografie (DE-588)4020216-1 gnd Räumliche Statistik (DE-588)4386767-4 gnd |
| subject_GND | (DE-588)4038971-6 (DE-588)4020216-1 (DE-588)4386767-4 |
| title | Spatial statistical methods for geography |
| title_auth | Spatial statistical methods for geography |
| title_exact_search | Spatial statistical methods for geography |
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| title_full | Spatial statistical methods for geography Peter A. Rogerson |
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| title_full_unstemmed | Spatial statistical methods for geography Peter A. Rogerson |
| title_short | Spatial statistical methods for geography |
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| topic_facet | Methode Geografie Räumliche Statistik |
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