名称

Bayesian Data Analysis, Second Edition (Texts in Statistical Science) (Hardcover)
by Andrew Gelman (Author), John B. Carlin (Author), Hal S. Stern (Author), Donald B. Rubin (Author)

大小：696 pages，10.9MB

格式：djvu
http://www.amazon.com/Bayesian-Analysis-Second-Statistical-Science/dp/158488388X/ref=sr_1_1/104-5895980-6364743?ie=UTF8&s=books&qid=1177874283&sr=8-1

Publisher: Chapman & Hall/CRC; 2 edition (July 29, 2003)

Language: English

ISBN-10: 158488388X

ISBN-13: 978-1584883883
[usemoney=15][/usemoney]

目录：（下面的目录内容是OCR所得，因此有很多单词中出现了多余的空格，另外有些词识别错误。但是我认为让网友们辨别清楚这是否是他们所需要的书是毫无问题的。我所发布的djvu文件文字清晰，排版正确，没有问题。）

Contents

List o f models

List o f exam p les

P refac e

P a r t I: Fundam ent als o f B aye sian Infere n ce

1 Background

1.1 Overview

1.2 General notation for statistical inference

1.3 Bayesian inference

1.4 Example: inference about a genetic probability

1.5 Probability as a measure of uncertainty

1.6 Example of probability assignment : football point spreads

1.7 Example of probability assignment: est imat ing the accuracy

of record linkage

1.8 Some usefu l results from probability theory

1.9 Summarizing inferences by simulation

1.10 Computation and software

1.11 Bibliographic note

1.12 Exercises

2 Sin gle-parame t e r models

2.1 Estimating a probability from binomial data

2.2 Posterior distribution as compromise between data and prior

information

2.3 Summarizing posterior inference

2.4 Informat ive prior distributions

2.5 Example: estimat ing the probability of a female birth given

placenta previa

2.0 Estimating the mean of a normal distribution with known

variance

2.7 Other standard single-parameter models

2.8 Example: informative prior distribution and multilevel st ructure

for est imat ing cancer rates

vii

x v

xvii

x ix

1

3

3

4

6

9

II

14

17

22

25

27

27

29

33

33

36

37

39

43

46

49

55

viii

2.9

2.10

2.11

Noninformative prior distributions

Bibli ographic note

Exercises

CONTENTS

61

65

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.G 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 t he posterior distribution 101

4.2 Large-sample theory 106

4.3 Counte rexamples to the theorems 108

4.4 Frequ ency evalua t ions of Bayesian inferences 111

4.5 Bibliographic note 113

4.6 Exercises 113

Part II: Fundamentals of Bayesian Data Analysis 115

5 Hierarchical models 11 7

5.1 Const ructing a parameterized prior distribution 118

5.2 Exchan geability and setting up hierarchical models 121

5.3 Computatio n with hierarchical models 125

5.4 Estimating an exchangeable set of parameters from a normal

model 131

5.5 Example: comhining information from educat ional test ing

experiments in eight schools 138

5.6 Hierarchical modeling applied to a meta-analysis 145

5.7 Bibliographi c note 150

5.8 Exerci ses 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 t he model consistent with data? Post erior predictive

checking 159

6.4 Graphical posterior pr edictive checks 165

CONTENTS ix

6.5

6.6

6.7

6.8

6.9

6.10

Numerical post erio r predicti ve checks

Model expansion

Model comparison

Model checking for the educational tes ting example

Bibliographic note

Exercises

172

177

179

186

190

192

7 Modeling accounting for data collection 197

7.1 Int roduction UJ7

7.2 Formal models for data collect ion 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 statis tical 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 est imation by ignoring some information 276

10.2 Usc of posterior simulat ions in Bayesian data analysis 276

10.3 Practical issues 278

10.4 Exercises 282

11 P osterior simula t ion 283

11 .1 Direct simulat ion 283

11.2 Markov chain simulat ion 285

11.3 The Gibbs sampler 287

x CONT ENTS

11.4 T he Metropolis and Metropolis-Hast ings algorithms 289

n .5 Building Markov chain algorithms using the Gibbs sampler

and Metropolis algorit hm 292

11.6 Infer ence and assessing converge nce 294

11.7 Example: the hierarchical normal model 299

n.8 Effi cient Gibbs samplers 302

11 .9 Efficient Metropolis jumping rul es 305

11.IORecommended st rategy for posterior simulat ion 307

11 .11 Bibliographic note 308

11.12 Exer cises 310

12 Approximations based on posterior modes 311

12.1 Finding posterior modes 312

12.2 T he normal and rela ted mixture approximatio ns 314

12.3 Finding marginal posterior modes using EM and related

algori t hms 317

12.4 Approximating conditional and marginal pos terior densities 32'1

12.5 Example: the hierarchical normal model (continued) 325

12.6 Bibliogr aphic note 331

12.7 Exerc ises 332

13 Special topics in computation 335

13.1 Advanced techniques for Markov chain simulat ion 335

13.2 Numerical integration 340

13.3 Importan ce sampling 342

13.4 Computing normaliz ing 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: estimat ing the advantage of incumbency in U.S.

Congressional elections 359

14.4 Goals of regression analys is 367

14.5 Assembling t he matrix of explanatory variables 369

14.6 Unequal variances and cor relations 372

14.7 Models for unequ al variances 375

14.8 Including prior informa tion 382

14.9 Bibliographic note 385

14.10 Exercises 385

CONTENTS xi

15 Hierarchical linear models 389

15.1 Regression coefficients exchangea ble in hatches 390

15.2 Example: forecasting U.S. Presidentia l elections 392

15.3 General nota t ion for hierarchical linea r 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 Int roduct ion 4 15

16.2 Standard generalized linear model likelihoods 416

16.3 Setting up and interpret ing generalized linear models 418

16.4 Computation 421

16.5 Example: hiera rchical Poisson regression for police stops 425

16.6 Example: hierarchical logist ic regr ession for political opinions 428

16.7 Models for multinomial responses 430

16.8 Loglinea r models for mul tivaria te discre te data 433

16.9 Bib liographic note 439

16.10 Exercises 440

17 Models for robust inference 443

17.1 Int roduction 443

17.2 Overd ispcrscd versions of standard probability models 445

17.3 Post erior inference and computation 448

17.4 Robust inference and sensitivity analysis for the ed uca tional

testing example 451

17.5 Robust regress ion using Student-s errors 455

17.u Bihliographic not e 457

17.7 Exercises 458

Part V: Specific Models and Problems 461

18 Mixture models 463

18.1 Int roduction 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 P r ior distributions for COVariance matrices 483

19.3 Hierarchical multivariate models 486

xii

19.4 Multivariate models for nonnor rnal data

19.5 Time series and spatia l models

19.6 Bibliographic not e

19.7 Exercises

CONTENTS

488

491

493

494 ·

20 Nonlinear models 497

20.1 Introducti on 497

20.2 Example: serial dilut ion assay 498

20.3 Example: population toxi cokinetics 504

20.4 Bibliographic note 514

20.5 Exercises 515

21 Models for missing data 517

21.1 Notation 517

21.2 Multipl e imputation 519

21.3 Missing data in th e 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 a nalysis 541

22.1 Bayesian decision theory in different contexts 542

22.2 Using regression predictions: incentives for telephone surveys 544

22.3 Multi stage decision maki ng: 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 Bib liographic note 568

22.7 Exercises 569

Appendixes 571

A Standard probability distributions 573

A.l Int rodu ction 573

A.2 Continuous distributions 573

A.3 Discrete distributions 582

A.4 Bibliograph ic note 584

B Outline of proofs of asym p t ot ic theorems 585

13 .1 Bibliographic note 589

C Example of computation in R and Bugs 591

C.I Getting started with R and Bugs 591

CONTENTS

C.2 Fi tt ing a hierarchical model in Bugs

C.3 Options in the Bugs implementation

CA Fitting a hierarchical model in R

C.5 Further comments on computat ion

C.6 Bibli ographic notc

References

Author index

Subject index

xiii

592

596

600

607

608

611

647

655

[此贴子已经被作者于2007-4-30 4:48:22编辑过]