Statistical analysis of spatial and spatio-temporal point patterns:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
CRC Press, Taylor & Francis
2014
|
| Edition: | 3. ed. |
| Series: | Monographs on statistics and applied probability
128 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXXI, 267 S. graph. Darst. |
| ISBN: | 9781466560239 |
Staff View
MARC
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Record in the Search Index
| _version_ | 1804151349231747072 |
|---|---|
| adam_text | Contents
List of Figures xv
List of Tables xxvii
Preface xxix
1 Introduction 1
1.1 Spatial point patterns.......................................... 1
1.2 Sampling ....................................................... 6
1.3 Edge-effects ................................................... 8
1.4 Complete spatial randomness..................................... 9
1.5 Objectives of statistical analysis ............................ 11
1.6 The Dirichlet tessellation .................................... 12
1.7 Monte Carlo tests ............................................. 13
1.8 Software ...................................................... 16
2 Preliminary testing 17
2.1 Tests of complete spatial randomness .......................... 17
2.2 Inter-event distances.......................................... 18
2.2.1 Analysis of Japanese black pine saplings............. 21
2.2.2 Analysis of redwood seedlings........................ 21
2.2.3 Analysis of biological cells............................ 22
2.2.4 Small distances......................................... 23
2.3 Nearest neighbour distances ............................... 24
2.3.1 Analysis of Japanese black pine saplings............. 25
2.3.2 Analysis of redwood seedlings........................... 25
2.3.3 Analysis of biological cells............................ 26
2.4 Point to nearest event distances .............................. 26
2.4.1 Analysis of Japanese black pine seedlings............ 28
2.4.2 Analysis of redwood seedlings........................... 28
2.4.3 Analysis of biological cells............................ 28
2.5 Quadrat counts ................................................ 29
2.5.1 Analysis of Japanese black pine seedlings............ 30
2.5.2 Analysis of redwood seedlings........................... 31
2.5.3 Analysis of biological cells............................ 32
IX
x Contents
2.6 Scales of pattern............................................ 32
2.6.1 Analysis of Lansing Woods data........................ 33
2.6.2 Scales of dependence.................................. 34
2.7 Recommendations.............................................. 35
3 Methods for sparsely sampled patterns 39
3.1 General remarks.............................................. 39
3.2 Quadrat counts .............................................. 40
3.2.1 Tests of CSR.......................................... 41
3.2.2 Estimators of intensity............................... 42
3.2.3 Analysis of Lansing Woods data........................ 42
3.3 Distance measurements ....................................... 43
3.3.1 Distribution theory under CSR......................... 44
3.3.2 Tests of CSR.......................................... 46
3.3.3 Estimators of intensity............................... 49
3.3.4 Analysis of Lansing Woods data........................ 50
3.3.5 Catana’s wandering quarter.......................... 51
3.4 Tests of independence.................................... 52
3.5 Recommendations.............................................. 53
4 Spatial point processes 55
4.1 Processes and summary descriptions........................... 55
4.2 Second-order properties...................................... 57
4.2.1 Univariate processes.................................. 57
4.2.2 Extension to multivariate processes................... 60
4.3 Higher order moments and nearest neighbour distributions . 60
4.4 The homogeneous Poisson process ............................. 61
4.5 Independence and random labelling ........................... 63
4.6 Estimation of second-order properties ....................... 64
4.6.1 Stationary processes.................................. 64
4.6.2 Estimating the pair correlation function.............. 71
4.6.3 Intensity-reweighted stationary processes ............ 72
4.6.4 Multivariate processes................................ 73
4.6.5 Examples.............................................. 74
4.7 Displaced amacrine cells in the retina of a rabbit .......... 76
4.8 Estimation of nearest neighbour distributions................ 78
4.8.1 Examples.............................................. 79
4.9 Concluding remarks........................................... 79
5 Nonparametric methods 83
5.1 Introduction .............................................. 83
5.2 Estimating weighted integrals of the second-order intensity . 83
Contents xi
5.3 Nonparametric estimation of a spatially varying intensity . . 84
5.3.1 Estimating spatially varying intensities for the Lansing
Woods data....................................... 87
5.4 Analysing replicated spatial point patterns ................... 90
5.4.1 Estimating the AT-function from replicated data .... 92
5.4.2 Between-group comparisons in designed experiments . 94
5.5 Parametric or nonparametric methods? .......................... 97
6 Models 99
6.1 Introduction .................................................. 99
6.2 Contagious distributions ..................................... 100
6.3 Poisson cluster processes .................................... 101
6.4 Inhomogeneous Poisson processes .............................. 104
6.5 Cox processes ................................................ 106
6.6 Trans-Gaussian Cox processes ................................. 109
6.7 Simple inhibition processes .................................. 110
6.8 Markov point processes ....................................... 112
6.8.1 Pairwise interaction point processes................... 114
6.8.2 More general forms of interaction............... 118
6.9 Other constructions .......................................... 118
6.9.1 Lattice-based processes ............................... 118
6.9.2 Thinned processes.................................... 119
6.9.3 Superpositions.................................. 120
6.9.4 Interactions in an inhomogeneous environment .... 121
6.10 Multivariate models........................................... 123
6.10.1 Marked point processes.......................... 123
6.10.2 Multivariate point processes.................... 123
6.10.3 How should multivariate models be formulated? .... 124
6.10.4 Cox processes.......................................... 125
6.10.5 Markov point processes................................. 128
7 Model-fitting using summary descriptions 131
7.1 Introduction ................................................ 131
7.2 Parameter estimation using the iif-function................... 132
7.2.1 Least squares estimation........................ 132
7.2.2 Simulated realisations of a Poisson cluster process . . 133
7.2.3 Procedure when K(t) is unknown.................. 134
7.3 Goodness-of-fit assessment using nearest neighbour distribu-
tions ............................................................ 135
7.4 Examples...................................................... 136
7.4.1 Redwood seedlings............................... 136
7.4.2 Bramble canes................................... 139
7.5 Parameter estimation via goodness-of-fit testing ............. 147
xii Contents
7.5.1 Analysis of hamster tumour data...................... 148
8 Model-fitting using likelihood-based methods 151
8.1 Introduction ................................................. 151
8.2 Likelihood inference for inhomogeneous Poisson processes . . 152
8.2.1 Fitting a trend surface to the Lansing Woods data . . 153
8.3 Likelihood inference for Markov point processes ............ 155
8.3.1 Maximum pseudo-likelihood estimation................... 156
8.3.2 Non-parametric estimation of a pairwise interaction
function.............................................. 158
8.3.3 Fitting a pairwise interaction point process to the dis-
placed amacrine cells........................................ 158
8.3.4 Monte Carlo maximum likelihood estimation ..... 160
8.3.5 The displaced amacrine cells re-visited................ 163
8.3.6 A bivariate model for the displaced amacrine cells . . 165
8.4 Likelihood inference for Cox processes........................ 167
8.4.1 Predictive inference in a log-Gaussian Cox process . . 169
8.4.2 Non-parametric estimation of an intensity surface: hick-
ories in Lansing Woods....................................... 170
8.5 Additional reading............................................ 172
9 Point process methods in spatial epidemiology 173
9.1 Introduction ............................................... 173
9.2 Spatial clustering ........................................... 176
9.2.1 Analysis of the North Humberside childhood leukaemia
data.................................................. 177
9.2.2 Other tests of spatial clustering...................... 178
9.3 Spatial variation in risk..................................... 179
9.3.1 Primary biliary cirrhosis in the North East of England 181
9.4 Point source models........................................... 182
9.4.1 Childhood asthma in north Derbyshire, England . . . 185
9.4.2 Cancers in North Liverpool............................. 186
9.5 Stratification and matching................................... 189
9.5.1 Stratified case-control designs........................ 189
9.5.2 Individually matched case-control designs.............. 191
9.5.3 Is stratification or matching helpful?................. 193
9.6 Disentangling heterogeneity and clustering ................... 193
10 Spatio-temporal point processes 195
10.1 Introduction ................................................ 195
10.2 Motivating examples ......................................... 196
10.2.1 Gastro-intestinal illness in Hampshire, UK............. 196
Contents xiii
10.2.2 The 2001 foot-and-mouth epidemic in Cumbria, UK . 198
10.2.3 Bovine tuberculosis in Cornwall, UK................ 198
10.3 A classification of spatio-temporal point patterns and processes 199
10.4 Second-order properties..................................... 202
10.5 Conditioning on the past ................................. 204
10.6 Empirical and mechanistic models............................ 207
11 Exploratory analysis 209
11.1 Introduction ............................................... 209
11.2 Animation .................................................. 210
11.3 Marginal and conditional summaries.......................... 210
11.3.1 Bovine tuberculosis in Cornwall, UK................. 210
11.4 Second-order properties.................................... 213
11.4.1 Stationary processes................................. 213
11.4.2 Intensity-reweighted stationary processes ........... 216
11.4.3 Campylobacteriosis in Lancashire, UK ......... 217
12 Empirical models and methods 223
12.1 Introduction .............................................. 223
12.2 Poisson processes .......................................... 224
12.3 Cox processes .............................................. 224
12.3.1 Separable and non-separable models................... 225
12.4 Log-Gaussian Cox processes ................................. 226
12.5 Inference .................................................. 227
12.6 Gastro-intestinal illness in Hampshire, UK ................. 227
12.7 Concluding remarks: point processes and geostatistics .... 230
13 Mechanistic models and methods 235
13.1 Introduction .............................................. 235
13.2 Conditional intensity and likelihood ....................... 235
13.3 Partial likelihood ....................................... 237
13.4 The 2001 foot-and-mouth epidemic in Cumbria, UK............. 238
13.5 Nesting patterns of Arctic terns ........................... 240
References 245
Index
263
|
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| language | English |
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| spelling | Diggle, Peter 1950- Verfasser (DE-588)134228014 aut Statistical analysis of spatial and spatio-temporal point patterns Peter J. Diggle 3. ed. Boca Raton [u.a.] CRC Press, Taylor & Francis 2014 XXXI, 267 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Monographs on statistics and applied probability 128 Spatial analysis (Statistics) Statistik (DE-588)4056995-0 gnd rswk-swf Mustererkennung (DE-588)4040936-3 gnd rswk-swf Mustererkennung (DE-588)4040936-3 s Statistik (DE-588)4056995-0 s DE-604 Monographs on statistics and applied probability 128 (DE-604)BV002494005 128 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026735789&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diggle, Peter 1950- Statistical analysis of spatial and spatio-temporal point patterns Monographs on statistics and applied probability Spatial analysis (Statistics) Statistik (DE-588)4056995-0 gnd Mustererkennung (DE-588)4040936-3 gnd |
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| title | Statistical analysis of spatial and spatio-temporal point patterns |
| title_auth | Statistical analysis of spatial and spatio-temporal point patterns |
| title_exact_search | Statistical analysis of spatial and spatio-temporal point patterns |
| title_full | Statistical analysis of spatial and spatio-temporal point patterns Peter J. Diggle |
| title_fullStr | Statistical analysis of spatial and spatio-temporal point patterns Peter J. Diggle |
| title_full_unstemmed | Statistical analysis of spatial and spatio-temporal point patterns Peter J. Diggle |
| title_short | Statistical analysis of spatial and spatio-temporal point patterns |
| title_sort | statistical analysis of spatial and spatio temporal point patterns |
| topic | Spatial analysis (Statistics) Statistik (DE-588)4056995-0 gnd Mustererkennung (DE-588)4040936-3 gnd |
| topic_facet | Spatial analysis (Statistics) Statistik Mustererkennung |
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