Bayesian smoothing and regression for longitudinal, spatial and event history data:
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Oxford [u.a.]
Oxford Univ. Press
2011
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Oxford statistical science series
36 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024149455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Umfang: | XVIII, 521 S. Ill., graph. Darst., Kt. |
| ISBN: | 9780199533022 0199533024 |
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Datensatz im Suchindex
| _version_ | 1819261641777217536 |
|---|---|
| adam_text | Titel: Bayesian smoothing and regression for longitudinal, spatial and event history data
Autor: Fahrmeir, Ludwig
Jahr: 2011
Contents
XV
List of Algorithms
List of Examples xvi
1. Introduction: Scope of the Book and Applications 1
1.1 Semiparametric regression 1
1.2 Applications 4
2. Basic Concepts for Smoothing and Semiparametric Regression 18
2.1 Time series smoothing 19
2.1.1 Gaussian Observation modeis 19
Penalized least-squares smoothing 20
Bayesian smoothing 23
2.1.2 Some modifications and extensions 27
Estimation of smoothing parameters and variances 27
Other model components 27
Correlated errors 28
Locally adaptive smoothing 29
Unequally spaced time-series observations 30
2.1.3 Non-Gaussian Observation modeis 30
2.2 Semiparametric regression based on penalized splines 34
2.2.1 Gaussian Observation modeis 34
Polynomial splines 35
Truncated power series and B-splines 36
Nonparametric regression based on polynomial splines 39
Characteristics of a spline fit 41
P-splines 42
Customized penalties 47
Bayesian P-splines 48
Bayesian inference 52
Degrees of freedom of a P-spline 55
2.2.2 Univariate non-Gaussian Observation modeis 57
Penalized lifcelihood estimation 58
Bayesian inference 60
Latent variable representations 63
2.2.3 Categorical observatioB modeis 67
Nominal response modeis 68
Cumulative modeis for ordinal responses 73
x Contents
Sequential modeis for ordinal responses 77
Penalised likelihood inference 79
Bayesian inference 81
2.2.4 Related smoothing approaches 82
Integral penalties 82
Smoothing splines 83
Bayesian Interpretation of smoothing splines 85
Reproducing kernel Hubert spaces 87
Other types of basis mnctions 89
2.3 Generaüzed additive models 90
2.3.1 Gaussian additive models 90
Simultaneous penalized least-squares (PLS) smoothing 92
Backfitting 93
Bayesian backfitting: the Gibbs sampler 94
2.3.2 Non-Gaussian additive models 100
2.4 Notes and further reading 104
3. Generaüzed Linear Mixed Models 107
3.1 Linear mixed models with Gaussian random efFects 108
3.1.1 Linear mixed models for longitudinal data 108
Advantages of mixed models 111
Marginal and conditional formulation 114
Multilevel models 115
3.1.2 General linear mixed models 116
3.1.3 Bayesian linear mixed models 117
3.1.4 Likelihood-based inference 119
Estimation and prediction 119
Estimation of regression coefficients for given variance
components 121
Maximum likelihood (ML) estimation of variance
components 122
REML estimation for the variance parameters 122
Details on REML estimation for variance parameters 124
Bayesian Interpretation of ML and REML estimation 125
Testing hypotheses 126
3.1.5 Bayesian inference 127
Empirical Bayes inference 127
Füll Bayes inference 128
Pull Bayes inference for longitudinal data 129
3.2 Linear mixed models with flexible random effects priors 138
3.2.1 Finite mixture models 139
Fünfte mixture of normals prior: the heterogeneity model 140
MCMC inference for finite mixture models 141
Penalized mixture of normals priors 142
Contents xi
3.2.2 Dirichlet processes 143
Dirichlet process: descriptive definition 145
Stick breaking representation 145
Posterior Dirichlet process 147
Predictive distribution and clustering property 148
Dirichlet process mixtures 149
3.2.3 LMM with DP-based random effects priors 150
Longitudinal data LMMs with DP random effects priors 150
Longitudinal data LMMs with DPM priors 153
3.3 Generaüzed linear mixed models 155
3.3.1 Generalized linear mixed models for longitudinal data 157
GLMMs for univariate responses 157
Marginal and conditional models 159
Interpretation of regression parameters 160
GLMMs for categorical responses 161
3.3.2 General mixed models for non-Gaussian responses 164
3.3.3 Likelihood-based and empirical Bayes inference 164
3.3.4 Füll Bayesian inference for longitudinal data 171
3.3.5 Longitudinal data GLMMs with flexible random
effects priors 174
GLMMs with DP random effects priors 174
GLMMs with DPM random effects priors 175
3.4 Notes and further reading 176
Semiparametric Mixed Models for Longitudinal Data 178
4.1 Semiparametric mixed models based on Gaussian priors 179
4.1.1 Observation models for univariate responses from
exponential families 179
Generalized additive mixed models 179
Varying coefficient mixed models 181
ANOVA type interactions 182
Generic representation 182
4.1.2 Observation models for categorical responses 183
4.1.3 Gaussian priors for regression parameters and functions 185
4.2 Estimation 187
4.2.1 Empirical Bayes inference 187
Intuitive example 187
Mixed model representation for P-splines 190
Mixed model representation for general penalized
smoothers 192
Mixed model-based estimation of SPMMs 196
Identifiability 200
Constrained smoothness priors 205
Credible intervals and bands 206
Tests on the functional form 207
xii Contents
4.2.2 Füll Bayes estimation with Gaussian priors for regression
parameters 212
Gaussian SPMMs 213
Exponential family SPMMs 219
Categorical SPMMs 222
Credible intervals and bands 225
4.3 Smoothing and correlation 229
Correlations induced by penalized smoothing approaches 230
Identifiability problems 233
Radial basis functions and correlated errors 237
Summary 238
4.4 Extensions based on non-Gaussian priors 238
4.4.1 SPMMs with DP-based random effects priors 238
4.4.2 Shrinkage priors for high-dimensional regression
parameters 245
Ridge prior 245
Lasso prior 247
Lq priors 254
Further examples 255
4.4.3 Locally adaptive priors for functions 256
Locally adaptive penalties 256
Knot selection strategies 261
4.5 Model choice and model checking 263
4.5.1 Bayes factors and model selection criteria 264
Bayes factors and marginal likelihoods 264
Methods for estimating Bayes factors and marginal
likelihoods 266
Information criteria: AIC, BIC and DIC 269
BIC 270
AIC 270
DIC 275
4.5.2 Predictive methods for model assessment 276
Alternative predictive distributions 277
Assessing calibration: PIT and BOT 278
Proper scoring rules 281
Custom summary statistics 282
Monte Carlo estimation of predictive measures 283
Posterior predictive goodness-of-fit assessment 284
Exact cross validatory predictive assessment 286
Approximate cross validatory predictive assessment 287
4.5.3 Predictor selection using spike and slab priors 290
Variable selection 291
Function selection 297
Covariance matrix selection for random effects 302
Contents xiii
4.6 Notes and further reading 303
4.6.1 Individual-specific curves and functional mixed models 303
4.6.2 Approximate Bayesian inference 304
Variational Bayes approaches 304
Integrated nested laplace approximation (INLA) 305
4.6.3 Further comments 306
5. Spatial Smoothing, Interactions and Geoadditive Regression 307
5.1 Spatial data structures 309
5.1.1 Point-referenced data: Continuous spatial information 309
5.1.2 Interaction surfaces 314
5.1.3 Areal data: Discrete spatial information 318
5.1.4 Continuous vs. discrete spatial information 321
5.1.5 Spatial regression models 322
5.1.6 Other types of spatial data 325
5.2 Discrete spatial data: Markov random fields 325
5.2.1 A heuristic spatial smoothness prior 326
5.2.2 Markov random fields 328
Definition of Markov random fields 328
Brook s lemma 330
Negpotential function and Hammersley-Clifford theorem 332
Auto-models 334
5.2.3 Gaussian Markov random fields/auto-normal models 336
Basis function representation of GMRFs 340
Direct vs. latent autoregressive models 344
5.2.4 Extended Markov random Seid models 346
5.3 Spatial smoothing approaches and interactions 347
5.3.1 Tensor product penalized splines 347
Tensor product bases 348
Kronecker product penalties for tensor product bases 352
Generalized penalty concepts 358
Null Spaces of bivariate penalties 362
Higher-order Markov random fields on regulär grids 364
Higher-order interactions 364
5.3.2 Radial bases 366
Space filling algorithm 370
Penalties for radial bases 371
5.3.3 Tensor products vs. radial bases 373
5.4 Continuous spatial data: Stationary Gaussian random fields 374
Model formulation 375
Correlation functions 378
Parametrie classes of correlations functions 381
Bochner s theorem 385
Range anisotropic correlation functions 386
Variogram 389
xiv Contents
Estimation of covariance and correlation parameters 391
Nonparametric covariogram and variogram estimation 392
Gaussian random fields as radial basis function smoothers 395
Identifiability in geostatistical models 396
Classical geostatistics 398
5.5 Geoadditive regression 399
Füll Bayes inference 400
Empirical Bayes inference 407
5.6 Notes and further reading 413
6. Event History Data 415
6.1 Survival data 419
6.1.1 Basic notions for continuous survival times 419
6.1.2 Censoring and truncation 420
6.1.3 Likelihood contributions for different types of censoring 424
6.1.4 Discrete-time survival data 425
6.2 Continuous-time hazard regression 428
6.2.1 Observation models, priors and likelihoods 430
Observation models 430
Priors 431
Likelihoods 432
6.2.2 Füll Bayes inference for right-censored observations 433
Piecewise exponential model 433
Models with general structured additive predictor 434
6.2.3 Empirical Bayes (EB) inference for right-censored
observations 444
6.2.4 Inference for interval-censored observations 451
6.3 Discrete-time hazard regression 455
6.4 Accelerated failure time models 464
6.4.1 Observation models, likelihoods and priors 466
Penalized Gaussian mixture (PGM) 467
AFT models with DP(M) priors 470
6.5 Multi-state models 470
6.5.1 Continuous-time transition rate models 471
6.5.2 Counting process representation and likelihood
contributions 472
6.5.3 Empirical and füll Bayes inference 474
6.5.4 Model checking based on martingale residuals 481
6.5.5 Discrete-time multi-state models 485
6.6 Notes and further reading 488
6.6.1 Models for correlated survival data 490
6.6.2 Joint modelling of longitudinal and event history data 492
Bibliography 495
Index 519
|
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| author | Fahrmeir, Ludwig 1945- Kneib, Thomas 1976- |
| author_GND | (DE-588)120635682 (DE-588)131555332 |
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| author_variant | l f lf t k tk |
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| bvnumber | BV039131120 |
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| ctrlnum | (OCoLC)707160221 (DE-599)HBZHT016843478 |
| dewey-full | 519.536 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.536 |
| dewey-search | 519.536 |
| dewey-sort | 3519.536 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV039131120 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T15:50:45Z |
| institution | BVB |
| isbn | 9780199533022 0199533024 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-024149455 |
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| owner_facet | DE-11 DE-19 DE-BY-UBM DE-188 DE-824 |
| physical | XVIII, 521 S. Ill., graph. Darst., Kt. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Oxford Univ. Press |
| record_format | marc |
| series | Oxford statistical science series |
| series2 | Oxford statistical science series |
| spellingShingle | Fahrmeir, Ludwig 1945- Kneib, Thomas 1976- Bayesian smoothing and regression for longitudinal, spatial and event history data Oxford statistical science series Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Glättung (DE-588)4157404-7 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| subject_GND | (DE-588)4144220-9 (DE-588)4157404-7 (DE-588)4129903-6 |
| title | Bayesian smoothing and regression for longitudinal, spatial and event history data |
| title_auth | Bayesian smoothing and regression for longitudinal, spatial and event history data |
| title_exact_search | Bayesian smoothing and regression for longitudinal, spatial and event history data |
| title_full | Bayesian smoothing and regression for longitudinal, spatial and event history data Ludwig Fahrmeir ; Thomas Kneib |
| title_fullStr | Bayesian smoothing and regression for longitudinal, spatial and event history data Ludwig Fahrmeir ; Thomas Kneib |
| title_full_unstemmed | Bayesian smoothing and regression for longitudinal, spatial and event history data Ludwig Fahrmeir ; Thomas Kneib |
| title_short | Bayesian smoothing and regression for longitudinal, spatial and event history data |
| title_sort | bayesian smoothing and regression for longitudinal spatial and event history data |
| topic | Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Glättung (DE-588)4157404-7 gnd Regressionsanalyse (DE-588)4129903-6 gnd |
| topic_facet | Bayes-Entscheidungstheorie Glättung Regressionsanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024149455&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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