Spatial processes: models & applications
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
London
Pion
1981
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002134901&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | 266 S. graph. Darst., Kt. |
| ISBN: | 0850860814 |
Internformat
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Datensatz im Suchindex
| _version_ | 1819317935825485824 |
|---|---|
| adam_text | Titel: Spatial processes
Autor: Cliff, Andrew D
Jahr: 1981
Contents
1 Measures of autocorrelation in the plane
1.1 Introduction 1
1.2 Concepts of autocorrelation 7
1.2.1 Spatial autocorrelation 7
1.3 Basic spatial autocorrelation measures 10
1.3.1 Measures for nominal data 11
1.3.2 Measures for ordinal and interval data 13
1.3.3 Choice of test statistic 14
1.3.4 Limitations of measures 15
1.4 The weighted coefficients 16
1.4.1 The form of the coefficients 16
1.4.2 Structure of the weights 17
1.5 Tests of significance 19
1.5.1 General procedures 19
1.5.2 Interpretation of the results 21
1.6 Space-time interactions 22
1.6.1 Clustering in time and space 22
1.6.2 Tests of significance 24
1.7 Examples 24
1.7.1 Map pattern analysis 24
1.7.2 Diffusion on graphs; measles in Cornwall 24
1.7.3 Space-time interactions; cholera in the metropolis 27
1.8 Conclusions 33
2 Distribution theory for the join-count, /, and c statistics
2.1 Introduction 34
2.1.1 General expressions for the moments 34
2.2 The join-count statistics 36
2.2.1 Mean and variance of BB and BW 38
2.2.2 Higher moments 40
2.3 The Moran and Geary statistics 42
2.3.1 The moments of I, given assumption N 42
2.3.2 The moments of I under assumption R 45
2.4 The distributions of the test statistics 46
2.4.1 The / and c statistics 47
2.4.2 The join counts under free sampling 51
2.4.3 Asymptotic normality under assumption R 52
2.4.4 The Poisson limit for BB joins 52
2.5 Evaluation of the distribution functions 53
2.5.1 Monte Carlo study for I 54
2.5.2 Monte Carlo study for c 56
2.6 Monte Carlo studies for the join-count statistics, k = 2 56
2.6.1 The experimental procedure 56
2.6.2 Analysis of the results 59
2.6.3 The Poisson approximation 61
2.6.4 The other join-count statistics 62
2.7 Monte Carlo tests 63
2.8 Conclusions 65
Contents
3 Map comparison with application to diffusion processes
3.1 Introduction 66
3.2 Map comparison 66
3.2.1 The test 66
3.2.2 Application to diffusion processes 68
3.3 Empirical example 71
3.3.1 The Hägerstrand model 71
3.3.2 Analysis of simulation results 74
3.3.3 Interpretation of the results 81
3.4 Other methods 84
3.5 Conclusions 85
4 The analysis of spatial point patterns
4.1 Introduction 86
4.1.1 Random or mapped data ? 87
4.2 The method of quadrat counts 87
4.2.1 The Poisson process 87
4.2.2 True or apparent contagion? 90
4.2.3 A study of settlement patterns 92
4.2.4 Implications for settlement geography 99
4.3 The study of pattern by using distances 99
4.3.1 The Poisson and other processes 100
4.3.2 Tests using distances 104
4.3.3 Reflexive pairs 106
4.3.4 Spacing of towns along the Mississippi 107
4.3.5 Estimation of intensity 109
4.4 Analysis of mapped data 111
4.4.1 First-order (or moment) methods for intensity surfaces 111
4.4.2 Distance-based methods 112
4.4.3 Second-order analysis 115
4.4.4 Spectral analysis 116
4.4.5 Analysis in space and time 117
4.5 Conclusions 117
5 Spatial correlograms and related methods
5.1 Introduction 118
5.2 Spatial correlograms H8
5.2.1 Theory 118
5.2.2 A regional application: measles in Cornwall 120
5.3 The spatial scale of a process 123
5.3.1 Greig-Smith s method 123
5.3.2 Other approaches 125
5.3.3 The variagram 126
5.4 Scale and correlation between processes 127
5.4.1 Model formulation 127
5.4.2 Negative estimates 130
5.4.3 An alternative approach 131
5.4.4 Empirical application: land use in London 131
Contents
5.5 Model identification 134
5.5.1 The partial correlogram 134
5.5.2 Computational aspects 135
5.5.3 Spatiotemporal correlograms 136
5.5.4 Correlograms and partial correlograms for the London land-use data 137
5.6 Estimation of the weights 139
5.7 Conclusions 140
6 Models for spatial processes
6.1 Introduction 141
6.1.1 Reaction or interaction? 141
6.2 Model specification 142
6.2.1 Trend-surface analysis 145
6.2.2 Autoregressive models 145
6.2.3 Whittle s model 146
6.2.4 The conditional approach 148
6.2.5 Moving-average models 149
6.2.6 Regionalised variables 151
6.2.7 Generation of random variables 152
6.3 Estimation procedures 153
6.3.1 First-order conditional autoregression 154
6.3.2 First-order simultaneous autoregression 159
6.3.3 Higher order autoregressive schemes 160
6.3.4 Moving-average models 160
6.3.5 Regionalised variables 162
6.4 Choice of tests for spatial autocorrelation 163
6.4.1 Asymptotic relative efficiency 164
6.4.2 The likelihood ratio test 166
6.4.3 Comparison of the I and c statistics 167
6.4.4 Hie join-count statistics 170
6.5 Empirical comparisons 173
6.5.1 Comparisons using regression residuals 173
6.5.2 Monte Carlo studies 174
6.6 Conclusions 178
Appendix on the major theorems used in chapter 6 179
7 Autocorrelation and inferential statistics
7.1 Introduction
7.2 Comparison of means
7.2.1 The two-sample case
7.2.2 A modified t test
7.2.3 Extension to k samples
7.3 Correlation and regression
7.3.1 Correlation
7.3.2 Regression analysis
7.4 Spatial varíate differencing
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| any_adam_object | 1 |
| author | Cliff, Andrew 1943- Ord, John Keith 1942- |
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| dewey-full | 519.537 |
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| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.537 |
| dewey-search | 519.537 |
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| dewey-tens | 510 - Mathematics |
| discipline | Soziologie Mathematik Geographie |
| format | Book |
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| id | DE-604.BV003378524 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T08:03:30Z |
| institution | BVB |
| isbn | 0850860814 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002134901 |
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| spellingShingle | Cliff, Andrew 1943- Ord, John Keith 1942- Spatial processes models & applications Analyse spatiale (Statistique) Analyse spatiale (statistique) ram Corrélation (statistique) ram Regionalanalyse (DE-588)4299244-8 gnd Analyse (DE-588)4122795-5 gnd Geografischer Raum (DE-588)4156686-5 gnd Modell (DE-588)4039798-1 gnd |
| subject_GND | (DE-588)4299244-8 (DE-588)4122795-5 (DE-588)4156686-5 (DE-588)4039798-1 |
| title | Spatial processes models & applications |
| title_auth | Spatial processes models & applications |
| title_exact_search | Spatial processes models & applications |
| title_full | Spatial processes models & applications A. D. Cliff & J. K. Ord |
| title_fullStr | Spatial processes models & applications A. D. Cliff & J. K. Ord |
| title_full_unstemmed | Spatial processes models & applications A. D. Cliff & J. K. Ord |
| title_short | Spatial processes |
| title_sort | spatial processes models applications |
| title_sub | models & applications |
| topic | Analyse spatiale (Statistique) Analyse spatiale (statistique) ram Corrélation (statistique) ram Regionalanalyse (DE-588)4299244-8 gnd Analyse (DE-588)4122795-5 gnd Geografischer Raum (DE-588)4156686-5 gnd Modell (DE-588)4039798-1 gnd |
| topic_facet | Analyse spatiale (Statistique) Analyse spatiale (statistique) Corrélation (statistique) Regionalanalyse Analyse Geografischer Raum Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002134901&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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