Handbook of Spatial Statistics (Chapman & Hall CRC Handbooks of Modern Statistical Methods)

Cover Page......Page 1
Handbooks Of Modern Statistical Methods......Page 3
Title: Handbook Of Spatial Statistics......Page 4
ISBN 9781420072877......Page 5
Contents......Page 6
Preface......Page 9
List Of Contributors......Page 11
Part I......Page 13
1.1 Antecedents......Page 15
1.2 Agricultural Field Trials......Page 17
1.3 Modeling Continuous Spatial Variation......Page 19
1.3.2 Forestry......Page 20
1.4.1 Spatial Interaction And The Statistical Analysis Of Lattice Systems......Page 21
1.4.2 Modeling Spatial Patterns......Page 22
1.5 Maturity: Spatial Statistics As Generic Statistical Modeling......Page 23
References......Page 24
Part II Continuous Spatial Variation......Page 27
2.1 Spatial Stochastic Processes......Page 29
2.2 Stationary And Intrinsically Stationary Processes......Page 30
2.3 Nugget Effect......Page 31
2.4 Bochner's Theorem......Page 32
2.5 Isotropic Covariance Functions......Page 33
2.7 Examples Of Isotropic Covariance Functions......Page 35
2.8 Prediction Theory For Second- Order Stationary Processes......Page 38
References......Page 39
3.1 Overview......Page 41
3.2 Geostatistical Model......Page 42
3.3 Provisional Estimation Of The Mean Function......Page 43
3.4 Nonparametric Estimation Of The Semivariogram......Page 45
3.5 Modeling The Semivariogram......Page 48
3.6 Reestimation Of The Mean Function......Page 52
3.7 Kriging......Page 53
References......Page 56
4.1 Overview......Page 57
4.2 Maximum Likelihood Estimation......Page 58
4.3 Reml Estimation......Page 60
4.4 Asymptotic Results......Page 61
4.5 Hypothesis Testing And Model Comparisons......Page 62
4.6 Computational Issues......Page 63
4.7 Approximate And Composite Likelihood......Page 64
4.8 Methods For Non- Gaussian Data......Page 66
References......Page 67
Contents......Page 69
5.1.1 Continuous Fourier Transform......Page 70
5.1.3.1 Mean Square Continuity......Page 71
5.1.3.2 The Spectral Representation Theorem......Page 72
5.1.3.3 Bochner’s Theorem......Page 73
5.1.4 Spectral Representation Of Isotropic Covariance Functions......Page 74
5.1.5 Principal Irregular Term......Page 75
5.2.2 Spherical Model......Page 76
5.2.4 Matern Class......Page 77
5.3.1 Periodogram......Page 80
5.3.1.1 Theoretical Properties of the Periodogram......Page 81
5.3.2 Lattice Data With Missing Values......Page 82
5.3.3 Least Squares Estimation In The Spectral Domain......Page 83
5.4 Likelihood Estimation In The Spectral Domain......Page 84
5.5 Case Study: Analysis Of Sea Surface Temperature......Page 85
5.5.2 Parameter Estimation......Page 86
References......Page 88
6.1 Asymptotics......Page 91
6.2 Estimation......Page 97
References......Page 99
7.1 Introduction......Page 101
7.2 An Overview of Hierarchical Modeling......Page 102
7.2.1 Data Models......Page 103
7.2.4 Hierarchical Spatial Models......Page 104
7.3 Hierarchical Gaussian Geostatistical Model......Page 105
7.3.1 Posterior Analysis......Page 106
7.3.2 Parameter Model Considerations......Page 107
7.3.4 Gaussian Geostatistical Example: Midwest U. S. Temperatures......Page 108
7.4 Hierarchical Generalized Linear Geostatistical Models......Page 111
7.4.1 Computational Considerations......Page 112
7.4.2 Non- Gaussian Data Example: Mapping Bird Counts......Page 113
7.5 Discussion......Page 116
References......Page 117
Contents......Page 119
8.1 Full- Rank Geostatistical Setup......Page 120
8.2 Reduced- Rank Random Effects Parameterizations......Page 121
8.3.1 Mcmc Approach......Page 122
8.4 Choice Of Expansion Matrix, H......Page 123
8.4.1.1 Karhunen– Loeve Expansion......Page 124
8.4.2.1 Kernel Basis Functions......Page 126
8.5.1 Non- Gaussian Data Models......Page 127
8.5.2 Spatiotemporal Processes......Page 128
References......Page 129
9.1 Overview......Page 131
9.2 Smoothing And Kernel- Based Methods......Page 132
9.3 Basis Function Models......Page 134
9.4 Process Convolution Models......Page 135
9.5 Spatial Deformation Models......Page 136
References......Page 139
10.1 Monitoring Environmental Processes......Page 143
10.2 Design Objectives......Page 144
10.3 Design Paradigms......Page 145
10.4.1 Simple Random Sampling ( Srs)......Page 146
10.4.3 Variable Probability Designs......Page 147
10.5.1 Estimation Of Covariance Parameters......Page 148
10.5.2 Estimation Of Mean Parameters: The Regression Model Approach......Page 150
10.5.4 Prediction And Process Model Inference......Page 152
10.5.5 Entropy- Based Design......Page 153
References......Page 157
Contents......Page 161
11.1.1 The Gaussian- Log- Gaussian Mixture Model......Page 162
11.1.2 Properties And Interpretation......Page 163
11.1.4 Correlation Function And Prior Distribution......Page 165
11.1.5 An Application To Spanish Temperature Data......Page 166
11.2.1 Stick- Breaking Priors......Page 167
11.2.2 Generalized Spatial Dirichlet Process......Page 169
11.2.3 Hybrid Dirichlet Mixture Models......Page 170
11.2.4 Order- Based Dependent Dirichlet Process......Page 171
11.2.5 Spatial Kernel Stick- Breaking Prior......Page 172
11.2.6 A Case Study: Hurricane Ivan......Page 175
References......Page 178
Part III Discrete Spatial Variation......Page 181
Contents......Page 183
12.1.2.1 Definition......Page 184
12.1.3.1 Conditional Properties......Page 185
12.1.3.2 Markov Properties......Page 186
12.1.4 Conditional Specification......Page 187
12.1.5 Mcmc Algorithms For Gmrfs......Page 189
12.1.5.1 Basic Ideas Behind Mcmc......Page 190
12.1.5.2 The Gibbs Sampler......Page 191
12.1.6 Multivariate Gmrfs......Page 192
12.1.7.1 Why Are Exact Algorithms Important?......Page 194
12.1.7.3 Sampling From A Gmrf......Page 196
12.1.7.4 Sampling From A Gmrf Conditioned On Linear Constraints......Page 197
12.1.7.6 Interpretation Of The Cholesky Triangle......Page 198
12.1.7.8 Reordering Techniques: Band Matrices......Page 199
12.1.7.9 Reordering Techniques: General Sparse Matrices......Page 200
12.1.7.10 Exact Calculations Of Marginal Variances......Page 202
12.1.7.11 General Recursions......Page 203
12.1.7.13 Correcting For Linear Constraints......Page 204
12.1.8.1 Background......Page 205
12.1.8.2 The Hammersley– Clifford Theorem......Page 206
12.1.9.1 Mcmc For Fixed......Page 208
12.1.9.2 Mcmc For Random......Page 209
References......Page 210
13.1 Introduction......Page 213
13.2 Gaussian Conditional Autoregressions......Page 214
13.2.1 Example......Page 215
13.2.2 Gaussian Conditional Autoregressions On Regular Arrays......Page 217
13.2.3 Example......Page 218
13.3 Non- Gaussian Conditional Autoregressions......Page 219
13.4 Intrinsic Autoregressions......Page 220
13.4.1 Normalizing Intrinsic Autoregressions......Page 221
13.4.2 Example......Page 222
13.4.4 Higher- Order Intrinsic Autoregressions......Page 223
13.5 Multivariate Gaussian Conditional Autoregressions......Page 226
References......Page 227
14.1 Background......Page 229
14.2.1 The Generalized Linear Model......Page 231
14.2.3 Spatial Random Effects......Page 232
14.2.4 Convolution Priors......Page 235
14.2.5 Alternative Formulations......Page 236
14.2.6 Additional Considerations......Page 237
14.3 Example: Sasquatch Reports In Oregon Andwashington......Page 238
14.4.1 Zero- Inflated Poisson Models......Page 243
14.4.2 Spatiotemporal Models......Page 244
14.4.3 Multivariate Car ( Mcar) Models......Page 247
14.4.4 Recent Developments......Page 248
Appendix......Page 249
References......Page 252
15.1 Introduction......Page 257
15.2.1 Static Models......Page 258
15.2.2 Dynamic Models......Page 262
15.3 Relations Between Spatial And Spatiotemporal Models......Page 263
15.4 Interpretation......Page 265
15.5 Spatial Varying Parameters, Dependence, And Impacts......Page 266
15.7 Computation......Page 267
15.8 Example......Page 268
15.9 Extensions......Page 270
References......Page 271
Part IV Spatial Point Patterns......Page 273
16.1.1 Introduction......Page 275
16.1.2 Characterization Of Point Process Distributions......Page 278
16.1.3 Campbell And Moment Measures......Page 279
16.1.4 Reduced And Higher-order Campbell Measures......Page 282
16.1.5 Palm Theory And Conditioning......Page 285
16.1.6 Finite Point Processes......Page 290
16.1.7 Gibbs Measures By Local Specification......Page 292
References......Page 293
17.1 Model Construction......Page 295
17.1.1 The Probability Generating Functional......Page 298
17.1.2 Thinning......Page 299
17.1.3 Translation......Page 300
17.2 Poisson Processes......Page 301
17.2.1 Nonhomogeneous Poisson Process......Page 302
17.2.2 The Cox Process......Page 303
17.3 Poisson Cluster Processes......Page 304
17.3.2 The Neyman– Scott Poisson Cluster Process......Page 305
17.4 Markov Point Processes......Page 306
References......Page 309
18.1 Introduction......Page 311
18.2.1 Quadrat Sampling......Page 312
18.2.2 Distance Sampling......Page 313
18.3 Monte Carlo Tests......Page 314
18.4 Nearest Neighbor Methods For Mapped Point Patterns......Page 315
18.5 Estimating A Spatially Varying Intensity......Page 317
18.6.1 Stationary Processes......Page 319
18.6.2 Nonstationary Processes......Page 321
18.7.1 Qualitative Marks: Multivariate Point Patterns......Page 322
18.7.1.1 Example: Displaced Amacrine Cells In The Retina Of A Rabbit......Page 323
18.8 Replicated Point Patterns......Page 325
References......Page 327
19.1 Introduction......Page 329
19.2 Setting And Notation......Page 330
19.3.1 Methods Based On First- Order Moment Properties......Page 331
19.3.2 Methods Based On Second- Order Moment Properties......Page 332
19.3.3 Example: Tropical Rain Forest Trees......Page 333
19.3.4 Pseudo- Likelihood......Page 334
19.4.1 Gibbs Point Processes......Page 336
19.4.2 Example: Ants' Nests......Page 337
19.4.3 Cluster And Cox Processes......Page 339
19.5.1 Example: Reseeding Plants......Page 341
19.5.2 Cluster And Cox Processes......Page 343
19.5.3 Gibbs Point Processes......Page 344
19.5.4 Example: Cell Data......Page 345
References......Page 347
Contents......Page 351
20.1.1 Appropriateness Of Point Process Methods......Page 352
20.1.2 The Sampling Design......Page 353
20.2.1 Intensity......Page 354
20.2.2 Interaction......Page 355
20.2.3 Intensity And Interaction......Page 356
20.2.4 Confounding Between Intensity And Interaction......Page 357
20.2.5 Scope Of Inference......Page 358
20.3.1 Exploratory Analysis Of Intensity......Page 359
20.3.2 Exploratory Analysis Of Dependence On Covariates......Page 361
20.3.3 Exploratory Analysis Of Interpoint Interaction......Page 362
20.3.3.1 Analysis Assuming Stationarity......Page 363
20.3.3.2 Full Exploratory Analysis......Page 364
20.4 Modeling Tools......Page 365
20.4.1 Parametric Models Of Intensity......Page 366
20.4.2 Multilevel Models For Clustering......Page 367
20.4.3 Finite Gibbs Models......Page 369
20.5 Formal Inference......Page 372
20.5.2 Formal Inference About Model Parameters......Page 373
20.6.1 Intensity Residuals......Page 374
20.6.2 Validation Of Poisson Models......Page 376
20.6.3 Validation Of Multilevel Models......Page 377
20.7.1 Packages For Spatial Statistics In......Page 378
References......Page 379
Contents......Page 383
21.1.1 Multivariate Point Patterns......Page 384
21.1.2 Marked Point Patterns......Page 385
21.2.2 Responses And Covariates......Page 387
21.2.3 Modeling Approaches......Page 388
21.2.4 Kinds Of Marks......Page 389
21.3.2 Marked Point Processes......Page 390
21.3.4 Intensity......Page 391
21.3.5 Stationary Marked Point Processes......Page 392
21.4 Exploratory Analysis Of Intensity......Page 393
21.4.1 Intensity For Multitype Point Patterns......Page 394
21.4.2 Intensity For Marked Point Patterns With Real- Valued Marks......Page 396
21.5.1.1 Random Marking......Page 397
21.5.2 Stationary Poisson Marked Point Process......Page 398
21.5.3 Fitting Poisson Models......Page 399
21.6 Exploring Interaction In Multivariate Point Patterns......Page 400
21.6.1.1 A Pair Of Types......Page 401
21.6.1.2 One Type to Any Type......Page 402
21.6.3 Nonstationary Patterns......Page 403
21.7.1 Mark Correlation Function......Page 404
21.7.2 Mark Variogram......Page 405
21.7.3 Dependence Between Marks And Locations......Page 406
21.8.1.1 Independence Of Components......Page 407
21.8.1.2 Random Labeling......Page 408
21.9.2 Mark- Dependent Thinning......Page 409
21.9.4.1 Conditional Intensity......Page 410
21.9.4.4 Mark- Dependent Pairwise Interactions......Page 411
21.9.4.5 Pseudolikelihood For Multitype Gibbs Processes......Page 412
References......Page 413
22.1.1 Inferential Goals: What Are We Looking For?......Page 415
22.1.2 Available Data: Cases And Controls......Page 416
22.1.3 Clusters And Clustering......Page 417
22.1.4 Dataset......Page 418
22.2.1 Spatial Scan Statistics......Page 420
22.2.1.1 Application To The Chagas Disease Vector Data......Page 422
22.2.2 Comparing First- Order Properties......Page 423
22.2.2.1 Application To The Chagas Disease Vector Data......Page 424
22.3 Detecting Clustering......Page 426
22.3.1 Application To The Chagas Disease Vector Data......Page 429
22.4 Discussion......Page 431
References......Page 433
Part V Spatio-Temporal Processes......Page 437
23.1 Introduction......Page 439
23.2 Physically Inspired Probability Models For Space– Time Processes......Page 440
23.3 Gaussian Spatio- Temporal Processes......Page 441
23.4 Bochner's Theorem And Cressie– Huang Criterion......Page 442
23.5 Properties Of Space– Time Covariance Functions......Page 443
23.6 Nonseparable Stationary Covariance Functions......Page 444
23.8 Case Study: Irish Wind Data......Page 445
References......Page 446
24.1 Dynamic Linear Models......Page 449
24.2 Space Varying State Parameters......Page 452
24.3 Applications......Page 457
References......Page 459
25.1 Introduction......Page 461
25.2.1 Plotting The Data......Page 462
25.2.2 Moment- Based Summaries......Page 463
25.2.3 Campylobacteriosis In Lancashire, U. K.......Page 464
25.3.2 Cluster Processes......Page 467
25.3.3.2 Spatial Epidemic Processes......Page 469
25.4 The Likelihood Function......Page 470
25.5 Discussion And Further Reading......Page 471
References......Page 472
26.1 Introduction......Page 475
26.2.2 Brownian Motion......Page 476
26.2.3 Monk Seal Movements......Page 477
26.3.1 Displays......Page 478
26.3.3 Stochastic Differential Equations......Page 479
26.3.4 Potential Function Approach......Page 480
26.4 Inference Methods......Page 482
26.5 Difficulties That Can Arise......Page 483
26.7 Other Models......Page 484
26.8 Summary......Page 485
References......Page 486
27.1 Introduction......Page 489
27.2 Bayesian Formulation Of Data Assimilation......Page 490
27.2.4 Assimilation Cycle......Page 491
27.2.5 Sequential Updating......Page 492
27.3.1 The Kf Update Step......Page 493
27.3.4 Problems In Implementation Of The Kf......Page 494
27.4.1 Ensemble Update......Page 495
27.4.4 Localization Of The Ensemble Covariance......Page 497
27.5.1 Three- Dimensional Variational Assimilation......Page 498
27.6.2 Covariance Localization And Inflation......Page 500
27.6.3 Assimilation With The Community Atmospheric Model......Page 501
References......Page 503
Part VI Additional Topics......Page 505
28.1 Introduction......Page 507
28.2 Classical Multivariate Geostatistics......Page 508
28.2.1 Cokriging......Page 509
28.2.2 Intrinsic Multivariate Correlation And Nested Models......Page 511
28.3 Some Theory For Cross- Covariance Functions......Page 512
28.4 Separable Models......Page 514
28.5 Co- Regionalization......Page 515
28.6 Conditional Development Of The Lmc......Page 516
28.8 Bayesian Multivariate Spatial Regression Models......Page 517
28.8.1 An Illustration......Page 518
28.9 Other Constructive Approaches......Page 520
28.9.1 Kernel Convolution Methods......Page 522
28.9.3 Convolution Of Covariance Functions Approaches......Page 524
References......Page 525
29.1 Introduction......Page 529
29.2 Historical Perspective......Page 531
29.3.1 The Block Average......Page 534
29.4 Nested Block- Level Modeling......Page 538
29.5 Nonnested Block- Level Modeling......Page 539
29.6 Misaligned Regression Modeling......Page 542
29.6.1 A Misaligned Regression Modeling Example......Page 543
29.7 Fusion Of Spatial Data......Page 548
References......Page 549
30.1 Introduction......Page 553
30.2 Motivating Example......Page 554
30.3 Ecological Bias: Introduction......Page 556
30.4 Ecological Bias: Pure Specification Bias......Page 557
30.5 Ecological Bias: Confounding......Page 559
30.6 Combining Ecological And Individual Data......Page 561
30.7 Example Revisited......Page 563
30.8 Spatial Dependence And Hierarchical Modeling......Page 564
30.9 Example Revisited......Page 565
30.11 Concluding Remarks......Page 566
Acknowledgments......Page 567
References......Page 568
31.1 Introduction......Page 571
31.2 Directional Finite Difference And Derivative Processes......Page 573
31.3 Inference For Finite Differences And Gradients......Page 574
31.4 Illustration: Inference For Differences And Gradients......Page 575
31.5.1 Gradients Along Parametric Curves......Page 577
31.6 Illustration: Spatial Boundaries For Invasive Plant Species......Page 580
31.7 A Stochastic Algorithm For Constructing Boundaries......Page 583
31.8.1 Areal Wombling: A Brief Overview......Page 584
31.9 Concluding Remarks......Page 585
References......Page 586
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