Bayesian data analysis:
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
London [u.a.]
Chapman & Hall
1995
|
| Ausgabe: | 1. ed. |
| Schriftenreihe: | Texts in statistical science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIX, 526 S. graph. Darst. |
| ISBN: | 0412039915 |
Internformat
MARC
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| 245 | 1 | 0 | |a Bayesian data analysis |c Andrew Gelman ... |
| 250 | |a 1. ed. | ||
| 264 | 1 | |a London [u.a.] |b Chapman & Hall |c 1995 | |
| 300 | |a XIX, 526 S. |b graph. Darst. | ||
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| 650 | 7 | |a Methode van Bayes |2 gtt | |
| 650 | 4 | |a Statistique bayésienne | |
| 650 | 7 | |a Statistique bayésienne |2 ram | |
| 650 | 4 | |a Statistique mathématique | |
| 650 | 7 | |a analyse bayesienne |2 inriac | |
| 650 | 7 | |a inférence statistique |2 inriac | |
| 650 | 7 | |a méthode Bayes |2 inriac | |
| 650 | 7 | |a statistique appliquée |2 inriac | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Mathematical statistics | |
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Datensatz im Suchindex
| _version_ | 1804124840780627968 |
|---|---|
| adam_text | Contents
List of models xi
List of examples xiii
Preface xv
Part I: Fundamentals of Bayesian Inference 1
1 Background 3
1.1 Overview 3
1.2 General notation for statistical inference 4
1.3 Bayesian inference 7
1.4 Example: inference about a genetic probability 10
1.5 Probability as a measure of uncertainty 12
1.6 Example of probability assignment: football point spreads 15
1.7 Some useful results from probability theory IS
1.8 Summarizing inferences by simulation 21
1.9 Bibliographic note 24
1.10 Exercises 25
2 Single parameter models 28
2.1 Estimating a probability from binomial data 28
2.2 Posterior distribution as compromise between data and
prior information 32
2.3 Summarizing posterior inference 33
2.4 Informative prior distributions 34
2.5 Example: estimating the probability of a female birth given
placenta previa 39
2.6 Estimating the mean of a normal distribution with known
variance 42
2.7 Other standard single parameter models 45
2.8 Noninformative prior distributions 52
vi CONTENTS
2.9 Bibliographic note 57
2.10 Exercises 58
3 Introduction to multiparameter models 65
3.1 Averaging over nuisance parameters 65
3.2 Normal data with a noninformative prior distribution 66
3.3 Normal data with a conjugate prior distribution 71
3.4 Normal data with a semi conjugate prior distribution 73
3.5 The multinomial model 76
3.6 The multivariate normal model 78
3.7 Example: analysis of a bioassay experiment 82
3.8 Summary of elementary multiparameter modeling and
computation 86
3.9 Bibliographic note 87
3.10 Exercises 88
4 Large sample inference and connections to standard statis¬
tical methods 94
4.1 Normal approximations to the posterior distribution 94
4.2 Large sample theory 100
4.3 Counterexamples to the theorems 101
4.4 Frequency evaluations of Bayesian inferences 104
4.5 Bayesian interpretations of other statistical methods 106
4.6 Bibliographic note 111
4.7 Exercises 112
Part II: Fundamentals of Bayesian Data Analysis 117
5 Hierarchical models 119
5.1 Constructing a parameterized prior distribution 120
5.2 Exchangeability and setting up hierarchical models 123
5.3 Computation with hierarchical models 128
5.4 Estimating an exchangeable set of parameters from a normal
model 134
5.5 Example: combining information from educational testing
experiments in eight schools 141
5.6 Hierarchical modeling applied to a meta analysis 148
5.7 Bibliographic note 154
5.8 Exercises 156
6 Model checking and sensitivity analysis 161
6.1 The place of model checking and sensitivity analysis in
applied Bayesian statistics 161
6.2 Principles and methods of model checking 162
CONTENTS vii
6.3 Checking a model by comparing data to the posterior
predictive distribution 167
6.4 Sensitivity analysis 174
6.5 Comparing a discrete set of models using Bayes factors 175
6.6 Model expansion 177
6.7 Practical advice 179
6.8 Model checking for the educational testing example 179
6.9 Bibliographic note 183
6.10 Exercises 185
7 Study design in Bayesian analysis 190
7.1 Introduction 190
7.2 Relevance of design or data collection: simple examples 192
7.3 Formal models for data collection 194
7.4 Ignorability 199
7.5 Designs that are ignorable and known with no covariates,
including simple random sampling and completely random¬
ized experiments 200
7.6 Designs that are ignorable and known given covariates,
including stratified sampling and randomized block experi¬
ments 205
7.7 Designs that are ignorable and unknown, such as exper¬
iments with nonrandom treatment assignments based on
fully observed covariates 213
7.8 Designs that are nonignorable and known, such as censoring 215
7.9 Designs that are nonignorable and unknown, including
observational studies and unintentional missing data 219
7.10 Sensitivity and the role of randomization 221
7.11 Discussion 224
7.12 Bibliographic note 224
7.13 Exercises 225
8 Introduction to regression models 233
8.1 Introduction and notation 233
8.2 Bayesian justification of conditional modeling 235
8.3 Bayesian analysis of the classical regression model 235
8.4 Example: estimating the advantage of incumbency in U.S.
Congressional elections 240
8.5 Goals of regression analysis 248
8.6 Assembling the matrix of explanatory variables 250
8.7 Unequal variances and correlations 253
8.8 Models for unequal variances (heteroscedasticity) 257
8.9 Including prior information 259
8.10 Hierarchical linear models 262
viii CONTENTS
8.11 Bibliographic note 262
8.12 Exercises 263
Part III: Advanced Computation 267
9 Approximations based on posterior modes 269
9.1 Introduction 269
9.2 Crude estimation by ignoring some information 270
9.3 Finding posterior modes 271
9.4 The normal and related mixture approximations 274
9.5 Finding marginal posterior modes using EM and related
algorithms 276
9.6 Approximating the conditional posterior density, p(7|0,?/) 283
9.7 Approximating p( j y) using an analytic approximation to
p(7l0.y) 283
9.8 Example: the hierarchical normal model 284
9.9 Example: a hierarchical logistic regression model for rat
tumor rates 291
9.10 Bibliographic note 298
9.11 Exercises 298
10 Posterior simulation and integration 300
10.1 Posterior inference from simulation 300
10.2 Direct simulation 302
10.3 Numerical integration 305
10.4 Computing normalizing factors 308
10.5 Improving an approximation using importance resampling 312
10.6 Example: hierarchical logistic regression (continued) 313
10.7 Bibliographic note 316
10.8 Exercises 317
11 Markov chain simulation 320
11.1 Introduction 320
11.2 The Metropolis algorithm and its generalizations 322
11.3 The Gibbs sampler and related methods based on alternating
conditional sampling 326
11.4 Inference and assessing convergence from iterative simulation 329
11.5 Constructing efficient simulation algorithms 333
11.6 Example: the hierarchical normal model (continued) 335
11.7 Example: linear regression with several unknown variance
parameters 337
11.8 Bibliographic note 343
11.9 Exercises 344
CONTENTS ix
Part IV: Specific Models 345
12 Models for robust inference and sensitivity analysis 347
12.1 Introduction 347
12.2 Overdispersed versions of standard probability models 349
12.3 Posterior inference and computation 352
12.4 Robust inference and sensitivity analysis for the educational
testing example 354
12.5 Robust regression using Student i errors 360
12.6 Bibliographic note 362
12.7 Exercises 363
13 Hierarchical linear models 366
13.1 Regression coefficients exchangeable in batches 367
13.2 Example: forecasting U.S. Presidential elections 369
13.3 General notation and computation for hierarchical linear
models 376
13.4 Hierarchical modeling as an alternative to selecting explana¬
tory variables 379
13.5 Bibliographic note 380
13.6 Exercises 381
14 Generalized linear models 384
14.1 Introduction 384
14.2 Standard generalized linear model likelihoods 386
14.3 Setting up and interpreting generalized linear models 387
14.4 Bayesian nonhierarchical and hierarchical generalized linear
models 388
14.5 Computation 389
14.6 Models for multinomial responses 393
14.7 Loglinear models for multivariate discrete data 397
14.8 Bibliographic note 403
14.9 Exercises 404
15 Multivariate models 407
15.1 Introduction 407
15.2 Linear regression with multiple outcomes 407
15.3 Hierarchical multivariate models 410
15.4 Multivariate models for nonnormal data 412
15.5 Time series and spatial models 415
15.6 Bibliographic note 418
15.7 Exercises 419
16 Mixture models 420
x CONTENTS
16.1 Introduction 420
16.2 Setting up the model 421
16.3 Computation 424
16.4 Example: modeling reaction times of schizophrenics and
nonschizophrenics 426
16.5 Bibliographic note 438
17 Models for missing data 439
17.1 Introduction 439
17.2 Notation for data collection in the context of missing data
problems 439
17.3 Computation and multiple imputation 441
17.4 Missing data in the multivariate normal and t models 443
17.5 Missing values with counted data 447
17.6 Example: an opinion poll in Slovenia 448
17.7 Inference using multiple imputation 453
17.8 Bibliographic note 454
17.9 Exercises 455
18 Concluding advice 456
18.1 Setting up probability models 456
18.2 Posterior inference 461
18.3 Model evaluation 462
18.4 Conclusion 468
18.5 Bibliographic note 469
Appendixes 471
A Standard probability distributions 473
A.I Introduction 473
A.2 Continuous distributions 473
A.3 Discrete distributions 482
A.4 Bibliographic note 483
B Outline of proofs of asymptotic theorems 484
B.I Bibliographic note 488
References 489
Author Index 513
Subject Index 518
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| physical | XIX, 526 S. graph. Darst. |
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| spelling | Bayesian data analysis Andrew Gelman ... 1. ed. London [u.a.] Chapman & Hall 1995 XIX, 526 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science Analyse des données ram Data-analyse gtt Inférence - Méthodes statistiques ram Methode van Bayes gtt Statistique bayésienne Statistique bayésienne ram Statistique mathématique analyse bayesienne inriac inférence statistique inriac méthode Bayes inriac statistique appliquée inriac Bayesian statistical decision theory Mathematical statistics Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Regressionsmodell (DE-588)4127980-3 gnd rswk-swf Nichtparametrisches Verfahren (DE-588)4339273-8 gnd rswk-swf 1\p (DE-588)4143413-4 Aufsatzsammlung gnd-content Bayes-Entscheidungstheorie (DE-588)4144220-9 s Bayes-Verfahren (DE-588)4204326-8 s Regressionsmodell (DE-588)4127980-3 s Nichtparametrisches Verfahren (DE-588)4339273-8 s 2\p DE-604 Gelman, Andrew 1965- Sonstige (DE-588)128832592 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006934084&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bayesian data analysis Analyse des données ram Data-analyse gtt Inférence - Méthodes statistiques ram Methode van Bayes gtt Statistique bayésienne Statistique bayésienne ram Statistique mathématique analyse bayesienne inriac inférence statistique inriac méthode Bayes inriac statistique appliquée inriac Bayesian statistical decision theory Mathematical statistics Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Regressionsmodell (DE-588)4127980-3 gnd Nichtparametrisches Verfahren (DE-588)4339273-8 gnd |
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| title | Bayesian data analysis |
| title_auth | Bayesian data analysis |
| title_exact_search | Bayesian data analysis |
| title_full | Bayesian data analysis Andrew Gelman ... |
| title_fullStr | Bayesian data analysis Andrew Gelman ... |
| title_full_unstemmed | Bayesian data analysis Andrew Gelman ... |
| title_short | Bayesian data analysis |
| title_sort | bayesian data analysis |
| topic | Analyse des données ram Data-analyse gtt Inférence - Méthodes statistiques ram Methode van Bayes gtt Statistique bayésienne Statistique bayésienne ram Statistique mathématique analyse bayesienne inriac inférence statistique inriac méthode Bayes inriac statistique appliquée inriac Bayesian statistical decision theory Mathematical statistics Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Regressionsmodell (DE-588)4127980-3 gnd Nichtparametrisches Verfahren (DE-588)4339273-8 gnd |
| topic_facet | Analyse des données Data-analyse Inférence - Méthodes statistiques Methode van Bayes Statistique bayésienne Statistique mathématique analyse bayesienne inférence statistique méthode Bayes statistique appliquée Bayesian statistical decision theory Mathematical statistics Bayes-Entscheidungstheorie Bayes-Verfahren Regressionsmodell Nichtparametrisches Verfahren Aufsatzsammlung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006934084&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gelmanandrew bayesiandataanalysis |