Bayesian Methods: A Social and Behavioral Sciences Approach, Second Edition(Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences)

About the Book

The first edition of Bayesian Methods: A Social and Behavioral Sciences Approach helped pave the way for Bayesian approaches to become more prominent in social science methodology. While the focus remains on practical modeling and basic theory as well as on intuitive explanations and derivations without skipping steps, this second edition incorporates the latest methodology and recent changes in software offerings.

New to the Second Edition

Two chapters on Markov chain Monte Carlo (MCMC) that cover ergodicity, convergence, mixing, simulated annealing, reversible jump MCMC, and coupling

Expanded coverage of Bayesian linear and hierarchical models

More technical and philosophical details on prior distributions

A dedicated R package (BaM) with data and code for the examples as well as a set of functions for practical purposes such as calculating highest posterior density (HPD) intervals

Requiring only a basic working knowledge of linear algebra and calculus, this text is one of the few to offer a graduate-level introduction to Bayesian statistics for social scientists. It first introduces Bayesian statistics and inference, before moving on to assess model quality and fit. Subsequent chapters examine hierarchical models within a Bayesian context and explore MCMC techniques and other numerical methods. Concentrating on practical computing issues, the author includes specific details for Bayesian model building and testing and uses the R and BUGS software for examples and exercises.

Table of Contents:
PREFACES

BACKGROUND AND INTRODUCTION
Introduction
Motivation and Justification
Why Are We Uncertain about Probability?
Bayes' Law
Conditional Inference with Bayes' Law
Historical Comments
The Scientific Process in Our Social Sciences
Introducing Markov Chain Monte Carlo Techniques
Exercises

SPECIFYING BAYESIAN MODELS
Purpose
Likelihood Theory and Estimation
The Basic Bayesian Framework
Bayesian "Learning"
Comments on Prior Distributions
Bayesian versus Non-Bayesian Approaches
Exercises
Computational Addendum: R for Basic Analysis

THE NORMAL AND STUDENT'S-T MODELS
Why Be Normal?
The Normal Model with Variance Known
The Normal Model with Mean Known
The Normal Model with Both Mean and Variance Unknown
Multivariate Normal Model, µ and S Both Unknown
Simulated Effects of Differing Priors
Some Normal Comments
The Student's t Model
Normal Mixture Models
Exercises
Computational Addendum: Normal Examples

THE BAYESIAN LINEAR MODEL
The Basic Regression Model
Posterior Predictive Distribution for the Data
The Bayesian Linear Regression Model with Heteroscedasticity
Exercises
Computational Addendum

THE BAYESIAN PRIOR
A Prior Discussion of Priors
A Plethora of Priors
Conjugate Prior Forms
Uninformative Prior Distributions
Informative Prior Distributions
Hybrid Prior Forms
Nonparametric Priors
Bayesian Shrinkage
Exercises

ASSESSING MODEL QUALITY
Motivation
Basic Sensitivity Analysis
Robustness Evaluation
Comparing Data to the Posterior Predictive Distribution
Simple Bayesian Model Averaging
Concluding Comments on Model Quality
Exercises
Computational Addendum

BAYESIAN HYPOTHESIS TESTING AND THE BAYES' FACTOR
Motivation
Bayesian Inference and Hypothesis Testing
The Bayes' Factor as Evidence
The Bayesian Information Criterion (BIC)
The Deviance Information Criterion (DIC)
Comparing Posteriors with the Kullback-Leibler Distance
Laplace Approximation of Bayesian Posterior Densities
Exercises

MONTE CARLO METHODS
Background
Basic Monte Carlo Integration
Rejection Sampling
Classical Numerical Integration
Gaussian Quadrature
Importance Sampling/Sampling Importance Resampling
Mode Finding and the EM Algorithm
Survey of Random Number Generation
Concluding Remarks
Exercises
Computational Addendum: RR@R for Importance Sampling

BASICS OF MARKOV CHAIN MONTE CARLO
Who Is Markov and What Is He Doing with Chains?
General Properties of Markov Chains
The Gibbs Sampler
The Metropolis-Hastings Algorithm
The Hit-and-Run Algorithm
The Data Augmentation Algorithm
Historical Comments
Exercises
Computational Addendum: Simple R Graphing Routines for
MCMC

BAYESIAN HIERARCHICAL MODELS
Introduction to Multilevel Models
Standard Multilevel Linear Models
A Poisson-Gamma Hierarchical Model
The General Role of Priors and Hyperpriors
Exchangeability
Empirical Bayes
Exercises
Computational Addendum: Instructions for Running JAGS, Trade Data Model

SOME MARKOV CHAIN MONTE CARLO THEORY
Motivation
Measure and Probability Preliminaries
Specific Markov Chain Properties
Defining and Reaching Convergence
Rates of Convergence
Implementation Concerns
Exercises

UTILITARIAN MARKOV CHAIN MONTE CARLO
Practical Considerations and Admonitions
Assessing Convergence of Markov Chains
Mixing and Acceleration
Producing the Marginal Likelihood Integral from Metropolis-
Hastings Output
Rao-Blackwellizing for Improved Variance Estimation
Exercises
Computational Addendum: R Code for the Death Penalty Support Model and BUGS Code for the Military Personnel Model

ADVANCED MARKOV CHAIN MONTE CARLO
Simulated Annealing
Reversible Jump Algorithms
Perfect Sampling
Exercises

APPENDIX A: GENERALIZED LINEAR MODEL REVIEW
Terms
The Generalized Linear Model
Numerical Maximum Likelihood
Quasi-Likelihood
Exercises
R for Generalized Linear Models

APPENDIX B: COMMON PROBABILITY DISTRIBUTIONS

APPENDIX C: INTRODUCTION TO THE BUGS LANGUAGE
General Process
Technical Background on the Algorithm
WinBUGS Features
JAGS Programming

REFERENCES

AUTHOR INDEX
SUBJECT INDEX

About the Author :
Jeff Gill, University of California - Davis, USA, DAVIS CA, U.S.A

Review :
Autodidacts with the requisite background in calculus, statistics, and linear algebra probably would get the greatest benefit out of Gill [due to] breadth of relevant topics and in-depth coverage of MCMC issues ! --Michael Smithson, Journal of Educational and Behavioral Statistics, June 2010 The book will be very suitable for students of social science ! The reference list is carefully compiled; it will be very useful for a well-motivated reader. Altogether it is a very readable book, based on solid scholarship and written with conviction, gusto, and a sense of fun. --International Statistical Review (2009), 77, 2 The second edition of Bayesian Methods: A Social and Behavioral Sciences Approach is a major update from the original version. ! The result is a general audience text suitable for a first course in Bayesian statistics at the upper undergraduate level for highly quantitative students or at the graduate level for students in a wider variety of fields. ! Of the texts I have tried so far in [my] class, Gill's book has definitely worked the best for me. ! this book fills an important market segment for classes where the canonical Bayesian texts are a bit too advanced. The emphasis is on using Bayesian methods in practice, with topics introduced via higher-level discussions followed by implementation and theory. ! --Herbert K.H. Lee, University of California, Santa Cruz, The American Statistician, November 2008 Praise for the First Edition: This book is a brilliant and importantly very accessible introduction to the concept and application of Bayesian approaches to data analysis. The clear strength of the book is in making the concept practical and accessible, without necessarily dumbing it down. ! The coverage is also remarkable. --Dr. S.V. Subramanian, Harvard School of Public Health, Cambridge, Massachusetts, USA One of the signal contributions of Bayesian Methods: A Social and Behavioral Sciences Approach is to reintroduce Bayesian inference and computing to a general social sciences audience. This is an important contribution-one that will make demand for this book high ! Jeff Gill has gone some way toward reinventing the graduate-level methodology textbook ! Gill's treatment of the practicalities of convergence is a real service ! new users of the technique will appreciate this material. ! the inclusion of material on hierarchical modeling at first seems unconventional; its use in political science, while increasing, has been limited. However, Bayesian inference and MCMC methods are well-suited to these types of problems, and it is exactly these types of treatments that push the discipline in new directions. As noted, a number of monographs have appeared recently to reintroduce Bayesian inference to a new generation of computer-savvy statisticians. ! However, Gill achieves what these do not: a quality introduction and reference guide to Bayesian inference and MCMC methods that will become a standard in political methodology. --The Journal of Politics, November 2003