【下载】Bayesian Data Analysis~Chapman & Hall/CRC.2004

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Bayesian Data Analysis, Second Edition (Chapman & Hall/CRC Texts in Statistical Science) (Hardcover)

Andrew Gelman (Author), John B. Carlin (Author), Hal S. Stern (Author), Donald B. Rubin (Author)


Editorial Reviews
Review
If you have done some Bayesian modeling, using WinBUGS, and are anxious to take the next steps to more sophisticated modeling and diagnostics, then the book offers a wealth of advice… This is a book that challenges the user in its sophisticated approach toward data analysis in general and Bayesian methods in particular. I am thoroughly excited to have this book in hand to supplement course material and to offer research collaborators and clients at our consulting lab more sophisticated methods to solve their research problems.
-John Grego, University of South Carolina

Bayesian Data Analysis is easily the most comprehensive, scholarly, and thoughtful book on the subject, and I think will do much to promote the use of Bayesian methods
-Prof. David Blackwell, Department of Statistics, University of California, Berkeley

Praise for the first edition:
A tour de force... it is far more than an introductory text, and could act as a companion for a working scientist from undergraduate level through to professional life.
-Robert Matthews, Aston University, in New Scientist

an essential reference text for any applied statistician
-Stephen Brooks, University of Cambridge, in The Statistician

will contribute to closing the gap between scientists and statisticians
-Sander Greenland, UCLA, in American Journal of Epidemiology

an excellent teaching reference for advanced undergraduate and graduate courses
-Nicky Best, Imperial College School of Medicine, in Statistics in Medicine

Product Description
Incorporating new and updated information, this second edition of THE bestselling text in Bayesian data analysis continues to emphasize practice over theory, describing how to conceptualize, perform, and critique statistical analyses from a Bayesian perspective. Its world-class authors provide guidance on all aspects of Bayesian data analysis and include examples of real statistical analyses, based on their own research, that demonstrate how to solve complicated problems. Changes in the new edition include: ·Stronger focus on MCMC·Revision of the computational advice in Part III·New chapters on nonlinear models and decision analysis·Several additional applied examples from the authors' recent research·Additional chapters on current models for Bayesian data analysis such as nonlinear models, generalized linear mixed models, and more·Reorganization of chapters 6 and 7 on model checking and data collectionBayesian computation is currently at a stage where there are many reasonable ways to compute any given posterior distribution. However, the best approach is not always clear ahead of time. Reflecting this, the new edition offers a more pluralistic presentation, giving advice on performing computations from many perspectives while making clear the importance of being aware that there are different ways to implement any given iterative simulation computation. The new approach, additional examples, and updated information make Bayesian Data Analysis an excellent introductory text and a reference that working scientists will use throughout their professional life.

Product Details Hardcover: 696 pages Publisher: Chapman & Hall; 2 edition (July 29, 2003) Language: English ISBN-10: 158488388X ISBN-13: 978-1584883883

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关键词：Bayesian Analysis Analysi Chapman Analys Analysis Bayesian Chapman Hall CRC

Features
Provides a thorough update of the groundbreaking text in Bayesian statistics written by the major players in the fieldDescribes the principles of Bayesian analysis, emphasizing practical rather than theoretical issuesGuides readers through the entire process of Bayesian analysis using real, applied examplesConsiders a variety of models, including linear regression, hierarchical (random effects) models, robust models, generalized linear models, and mixture modelsAddresses issues ranging from incorporating survey design information to checking model adequacy, to handling missing data-all from a consistent and pragmatic Bayesian perspective

Summary
Incorporating new and updated information, this second edition of THE bestselling text in Bayesian data analysis continues to emphasize practice over theory, describing how to conceptualize, perform, and critique statistical analyses from a Bayesian perspective. Its world-class authors provide guidance on all aspects of Bayesian data analysis and include examples of real statistical analyses, based on their own research, that demonstrate how to solve complicated problems. Changes in the new edition include:

Stronger focus on MCMC
Revision of the computational advice in Part III
New chapters on nonlinear models and decision analysis
Several additional applied examples from the authors' recent research
Additional chapters on current models for Bayesian data analysis such as nonlinear models, generalized linear mixed models, and more
Reorganization of chapters 6 and 7 on model checking and data collection

Bayesian computation is currently at a stage where there are many reasonable ways to compute any given posterior distribution. However, the best approach is not always clear ahead of time. Reflecting this, the new edition offers a more pluralistic presentation, giving advice on performing computations from many perspectives while making clear the importance of being aware that there are different ways to implement any given iterative simulation computation. The new approach, additional examples, and updated information make Bayesian Data Analysis an excellent introductory text and a reference that working scientists will use throughout their professional life.

Contents

List of models xv

List of examples xvii

Preface xix

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 6

1.4 Example: inference about a genetic probability 9

1.5 Probability as a measure of uncertainty 11

1.6 Example of probability assignment: football point spreads 14

1.7 Example of probability assignment: estimating the accuracy of record linkage 17

1.8 Some useful results from probability theory 22

1.9 Summarizing inferences by simulation 25

1.10 Computation and software 27

1.11 Bibliographic note 27

1.12 Exercises 29

2 Single-parameter models 33

2.1 Estimating a probability from binomial data 33

2.2 Posterior distribution as compromise between data and prior information 36

2.3 Summarizing posterior inference 37

2.4 Informative prior distributions 39

2.5 Example: estimating the probability of a female birth given placenta previa 43

2.6 Estimating the mean of a normal distribution with known variance 46

2.7 Other standard single-parameter models 49

2.8 Example: informative prior distribution and multilevel structure for estimating cancer rates 55

2.9 Noninformative prior distributions 61

2.10 Bibliographic note 65

2.11 Exercises 67

3 Introduction to multiparameter models 73

3.1 Averaging over ‘nuisance parameters’ 73

3.2 Normal data with a noninformative prior distribution 74

3.3 Normal data with a conjugate prior distribution 78

3.4 Normal data with a semi-conjugate prior distribution 80

3.5 The multinomial model 83

3.6 The multivariate normal model 85

3.7 Example: analysis of a bioassay experiment 88

3.8 Summary of elementary modeling and computation 93

3.9 Bibliographic note 94

3.10 Exercises 95

4 Large-sample inference and frequency properties of Bayesian inference 101

4.1 Normal approximations to the posterior distribution 101

4.2 Large-sample theory 106

4.3 Counterexamples to the theorems 108

4.4 Frequency evaluations of Bayesian inferences 111

4.5 Bibliographic note 113

4.6 Exercises 113

Part II: Fundamentals of Bayesian Data Analysis 115

5 Hierarchical models 117

5.1 Constructing a parameterized prior distribution 118

5.2 Exchangeability and setting up hierarchical models 121

5.3 Computation with hierarchical models 125

5.4 Estimating an exchangeable set of parameters from a normal model 131

5.5 Example: combining information from educational testing experiments in eight schools 138

5.6 Hierarchical modeling applied to a meta-analysis 145

5.7 Bibliographic note 150

5.8 Exercises 152

6 Model checking and improvement 157

6.1 The place of model checking in applied Bayesian statistics 157

6.2 Do the inferences from the model make sense? 158

6.3 Is the model consistent with data? Posterior predictive checking 159

6.4 Graphical posterior predictive checks 165

6.5 Numerical posterior predictive checks 172

6.6 Model expansion 177

6.7 Model comparison 179

6.8 Model checking for the educational testing example 186

6.9 Bibliographic note 190

6.10 Exercises 192

7 Modeling accounting for data collection 197

7.1 Introduction 197

7.2 Formal models for data collection 200

7.3 Ignorability 203

7.4 Sample surveys 207

7.5 Designed experiments 218

7.6 Sensitivity and the role of randomization 223

7.7 Observational studies 226

7.8 Censoring and truncation 231

7.9 Discussion 236

7.10 Bibliographic note 237

7.11 Exercises 239

8 Connections and challenges 247

8.1 Bayesian interpretations of other statistical methods 247

8.2 Challenges in Bayesian data analysis 252

8.3 Bibliographic note 255

8.4 Exercises 255

9 General advice 259

9.1 Setting up probability models 259

9.2 Posterior inference 264

9.3 Model evaluation 265

9.4 Summary 271

9.5 Bibliographic note 271

Part III: Advanced Computation 273

10 Overview of computation 275

10.1 Crude estimation by ignoring some information 276

10.2 Use of posterior simulations in Bayesian data analysis 276

10.3 Practical issues 278

10.4 Exercises 282

11 Posterior simulation 283

11.1 Direct simulation 283

11.2 Markov chain simulation 285

11.3 The Gibbs sampler 287

11.4 The Metropolis and Metropolis-Hastings algorithms 289

11.5 Building Markov chain algorithms using the Gibbs sampler and Metropolis algorithm 292

11.6 Inference and assessing convergence 294

11.7 Example: the hierarchical normal model 299

11.8 Efficient Gibbs samplers 302

11.9 Efficient Metropolis jumping rules 305

11.10 Recommended strategy for posterior simulation 307

11.11 Bibliographic note 308

11.12 Exercises 310

12 Approximations based on posterior modes 311

12.1 Finding posterior modes 312

12.2 The normal and related mixture approximations 314

12.3 Finding marginal posterior modes using EM and related algorithms 317

12.4 Approximating conditional and marginal posterior densities 324

12.5 Example: the hierarchical normal model (continued) 325

12.6 Bibliographic note 331

12.7 Exercises 332

13 Special topics in computation 335

13.1 Advanced techniques for Markov chain simulation 335

13.2 Numerical integration 340

13.3 Importance sampling 342

13.4 Computing normalizing factors 345

13.5 Bibliographic note 348

13.6 Exercises 349

Part IV: Regression Models 351

14 Introduction to regression models 353

14.1 Introduction and notation 353

14.2 Bayesian analysis of the classical regression model 355

14.3 Example: estimating the advantage of incumbency in U.S. Congressional elections 359

14.4 Goals of regression analysis 367

14.5 Assembling the matrix of explanatory variables 369

14.6 Unequal variances and correlations 372

14.7 Models for unequal variances 375

14.8 Including prior information 382

14.9 Bibliographic note 385

14.10 Exercises 385

15 Hierarchical linear models 389

15.1 Regression coefficients exchangeable in batches 390

15.2 Example: forecasting U.S. Presidential elections 392

15.3 General notation for hierarchical linear models 399

15.4 Computation 400

15.5 Hierarchical modeling as an alternative to selecting predictors 405

15.6 Analysis of variance 406

15.7 Bibliographic note 411

15.8 Exercises 412

16 Generalized linear models 415

16.1 Introduction 415

16.2 Standard generalized linear model likelihoods 416

16.3 Setting up and interpreting generalized linear models 418

16.4 Computation 421

16.5 Example: hierarchical Poisson regression for police stops 425

16.6 Example: hierarchical logistic regression for political opinions 428

16.7 Models for multinomial responses 430

16.8 Loglinear models for multivariate discrete data 433

16.9 Bibliographic note 439

16.10 Exercises 440

17 Models for robust inference 443

17.1 Introduction 443

17.2 Overdispersed versions of standard probability models 445

17.3 Posterior inference and computation 448

17.4 Robust inference and sensitivity analysis for the educational testing example 451

17.5 Robust regression using Student-t errors 455

17.6 Bibliographic note 457

17.7 Exercises 458

Part V: Specific Models and Problems 461

18 Mixture models 463

18.1 Introduction 463

18.2 Setting up mixture models 463

18.3 Computation 467

18.4 Example: reaction times and schizophrenia 468

18.5 Bibliographic note 479

19 Multivariate models 481

19.1 Linear regression with multiple outcomes 481

19.2 Prior distributions for covariance matrices 483

19.3 Hierarchical multivariate models 486

19.4 Multivariate models for nonnormal data 488

19.5 Time series and spatial models 491

19.6 Bibliographic note 493

19.7 Exercises 494

20 Nonlinear models 497

20.1 Introduction 497

20.2 Example: serial dilution assay 498

20.3 Example: population toxicokinetics 504

20.4 Bibliographic note 514

20.5 Exercises 515

21 Models for missing data 517

21.1 Notation 517

21.2 Multiple imputation 519

21.3 Missing data in the multivariate normal and t models 523

21.4 Example: multiple imputation for a series of polls 526

21.5 Missing values with counted data 533

21.6 Example: an opinion poll in Slovenia 534

21.7 Bibliographic note 539

21.8 Exercises 540

22 Decision analysis 541

22.1 Bayesian decision theory in different contexts 542

22.2 Using regression predictions: incentives for telephone surveys 544

22.3 Multistage decision making: medical screening 552

22.4 Decision analysis using a hierarchical model: home radon measurement and remediation 555

22.5 Personal vs. institutional decision analysis 567

22.6 Bibliographic note 568

22.7 Exercises 569

Appendixes 571

A Standard probability distributions 573

A.1 Introduction 573

A.2 Continuous distributions 573

A.3 Discrete distributions 582

A.4 Bibliographic note 584

B Outline of proofs of asymptotic theorems 585

B.1 Bibliographic note 589

C Example of computation in R and Bugs 591

C.1 Getting started with R and Bugs 591

C.2 Fitting a hierarchical model in Bugs 592

C.3 Options in the Bugs implementation 596

C.4 Fitting a hierarchical model in R 600

C.5 Further comments on computation 607

C.6 Bibliographic note 608

References 611

Author index 647

Subject index 655

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