Bayesian analysis for the social sciences / Simon Jackman.

Format:

Book

Author/Creator:

Jackman, Simon, 1966-

Contributor:

Wiley InterScience (Online service)

Alumni and Friends Memorial Book Fund.

Series:

Wiley series in probability and statistics

Language:

English

Subjects (All):

Social sciences--Statistical methods.

Social sciences.

Bayesian statistical decision theory.

Physical Description:

1 online resource (xxxiv, 564 pages) : illustrations.

Place of Publication:

Chichester, U.K. : Wiley, 2009.

System Details:

text file

Summary:

The first part of this book presents the foundations of Bayesian inference, via simple inferential problems in the social sciences: proportions, cross-tabulations, counts, means and regression analysis. A review of modern, simulation-based inference is presented with a detailed examination of the suite of computational tools (Markov chain Monte Carlo algorithms) that underlie the "Bayesian revolution" in contemporary statistics. Furthermore, the book introduces the general purpose Bayesian computer programs BUGS and JAGS along with numerous examples, and a detailed consideration of the art of using these programs in real-world settings.

The second half of the book focuses on intermediate to advanced applications in the social sciences, including hierarchical or "multi-level" models, models for discrete responses (binary, ordinal, and multinomial data), measurement models (factor analysis, item-response models, dynamic linear models), and mixture models, along with models that are interesting hybrids of these models. Each model is accompanied by worked examples using BUGS/JAGS, using data from political science, sociology, psychology, education, communications, economics and anthropology.

Each chapter is accompanied with exercises to further the students' understanding of Bayesian methods and applications. Extensive appendices provide important technical background and proofs of key theoretical propositions.

This book presents a forceful argument for the philosophical and practical utility of the Bayesian approach in many social science settings. Graduate and postgraduate students in such fields as political science, sociology, psychology, communications, education, and economics and statisticians will find much value in this book.

Contents:

Part I Introducing Bayesian Analysis 1

1 The foundations of Bayesian inference 3

1.1 What is probability? 3

1.1.1 Probability in classical statistics 4

1.1.2 Subjective probability1 5

1.2 Subjective probability in Bayesian statistics 7

1.3 Bayes theorem, discrete case 8

1.4 Bayes theorem, continuous parameter 13

1.4.1 Conjugate priors 15

1.4.2 Bayesian updating with irregular priors 16

1.4.3 Cromwell's Rule 18

1.4.4 Bayesian updating as information accumulation 19

1.5 Parameters as random variables, beliefs as distributions 21

1.6 Communicating the results of a Bayesian analysis 22

1.6.1 Bayesian point estimation 23

1.6.2 Credible regions 26

1.7 Asymptotic properties of posterior distributions 29

1.8 Bayesian hypothesis testing 31

1.8.1 Model choice 36

1.8.2 Bayes factors 37

1.9 From subjective beliefs to parameters and models 38

1.9.1 Exchangeability 39

1.9.2 Implications and extensions of de Finetti's Representation Theorem 42

1.9.3 Finite exchangeability 43

1.9.4 Exchangeability and prediction 43

1.9.5 Conditional exchangeability and multiparameter models 44

1.9.6 Exchangeability of parameters: hierarchical modeling 45

1.10 Historical note 46

2 Getting started: Bayesian analysis for simple models 49

2.1 Learning about probabilities, rates and proportions 49

2.1.1 Conjugate priors for probabilities, rates and proportions 51

2.1.2 Bayes estimates as weighted averages of priors and data 58

2.1.3 Parameterizations and priors 61

2.1.4 The variance of the posterior density 64

2.2 Associations between binary variables 67

2.3 Learning from counts 73

2.3.1 Predictive inference with count data 78

2.4 Learning about a normal mean and variance 80

2.4.1 Variance known 80

2.4.2 Mean and variance unknown 83

2.4.3 Conditionally conjugate prior 92

2.4.4 An improper, reference prior 93

2.4.5 Conflict between likelihood and prior 98

2.4.6 Non-conjugate priors 98

2.5 Regression models 99

2.5.1 Bayesian regression analysis 102

2.5.2 Likelihood function 103

2.5.3 Conjugate prior 104

2.5.4 Improper, reference prior 107

2.6 Further reading 124

Part II Simulation Based Bayesian Analysis 129

3 Monte Carlo methods 133

3.1 Simulation consistency 134

3.2 Inference for functions of parameters 140

3.3 Marginalization via Monte Carlo integration 142

3.4 Sampling algorithms 153

3.4.1 Inverse-CDF method 153

3.4.2 Importance sampling 156

3.4.3 Accept-reject sampling 159

3.4.4 Adaptive rejection sampling 163

3.5 Further reading 167

4 Markov chains 171

4.1 Notation and definitions 172

4.1.1 State space 173

4.1.2 Transition kernel 173

4.2 Properties of Markov chains 176

4.2.1 Existence of a stationary distribution, discrete case 177

4.2.2 Existence of a stationary distribution, continuous case 178

4.2.3 Irreducibility 179

4.2.4 Recurrence 182

4.2.5 Invariant measure 184

4.2.6 Reversibility 185

4.2.7 Aperiodicity 186

4.3 Convergence of Markov chains 187

4.3.1 Speed of convergence 189

4.4 Limit theorems for Markov chains 191

4.4.1 Simulation inefficiency 191

4.4.2 Central limit theorems for Markov chains 195

4.5 Further reading 196

5 Markov chain Monte Carlo 201

5.1 Metropolis-Hastings algorithm 201

5.1.1 Theory for the Metropolis-Hastings algorithm 202

5.1.2 Choosing the proposal density 204

5.2 Gibbs sampling 214

5.2.1 Theory for the Gibbs sampler 218

5.2.2 Connection to the Metropolis algorithm 221

5.2.3 Deriving conditional densities for the Gibbs sampler: statistical models as conditional independence graphs 225

5.2.4 Pathologies 229

5.2.5 Data augmentation 236

5.2.6 Missing data problems 237

5.2.7 The slice sampler 244

6 Implementing Markov chain Monte Carlo 251

6.1 Software for Markov chain Monte Carlo 251

6.2 Assessing convergence and run-length 252

6.3 Working with BUGS/JAGS from R 256

6.4 Tricks of the trade 261

6.4.1 Thinning 261

6.4.2 Blocking 264

6.4.3 Reparameterization 270

6.5 Other examples 272

6.6 Further reading 292

Part III Advanced Applications in the Social Sciences 299

7 Hierarchical Statistical Models 301

7.1 Data and parameters that vary by groups: the case for hierarchical modeling 301

7.1.1 Exchangeable parameters generate hierarchical models 305

7.1.2 ’Borrowing strength’ via exchangeability 307

7.1.3 Hierarchical modeling as a 'semi-pooling’ estimator 307

7.1.4 Hierarchical modeling as a 'shrinkage’ estimator 308

7.1.5 Computation via Markov chain Monte Carlo 310

7.2 ANOVA as a hierarchical model 317

7.2.1 One-way analysis of variance 317

7.2.2 Two-way ANOVA 329

7.3 Hierarchical models for longitudinal data 345

7.4 Hierarchical models for non-normal data 354

7.5 Multi-level models 362

8 Bayesian analysis of choice making 379

8.1 Regression models for binary responses 379

8.1.1 Probit model via data augmentation 380

8.1.2 Probit model via marginal data augmentation 389

8.1.3 Logit model 393

8.1.4 Binomial model for grouped binary data 395

8.2 Ordered outcomes 397

8.2.1 Identification 399

8.3 Multinomial outcomes 415

8.3.1 Multinomial logit (MNL) 415

8.3.2 Independence of irrelevant alternatives 423

8.4 Multinomial probit 424

8.4.1 Bayesian analysis via MCMC 426

9 Bayesian approaches to measurement 435

9.1 Bayesian inference for latent states 435

9.1.1 A formal role for prior information 436

9.1.2 Inference for many parameters 436

9.2 Factor analysis 438

9.2.1 Likelihood and prior densities 439

9.2.2 Identification 440

9.2.3 Posterior density 442

9.2.4 Inference over rank orderings of the latent variable 448

9.2.5 Incorporating additional information via hierarchical modeling 449

9.3 Item-response models 454

9.4 Dynamic measurement models 471

9.4.1 State-space models for [pooling the polls] 473

9.4.2 Bayesian inference 474

Part IV Appendices 489.

Notes:

Includes bibliographical references and indexes.

Electronic reproduction. Hoboken, N.J. Available via World Wide Web.

Description based on print version record.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

9780470686621

0470686626

Publisher Number:

99965899452

Access Restriction:

Restricted for use by site license.