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

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