3rd Edition

Bayesian Methods A Social and Behavioral Sciences Approach, Third Edition

By Jeff Gill Copyright 2015
    722 Pages 56 B/W Illustrations
    by Chapman & Hall

    An Update of the Most Popular Graduate-Level Introductions to Bayesian Statistics for Social Scientists

    Now that Bayesian modeling has become standard, MCMC is well understood and trusted, and computing power continues to increase, Bayesian Methods: A Social and Behavioral Sciences Approach, Third Edition focuses more on implementation details of the procedures and less on justifying procedures. The expanded examples reflect this updated approach.

    New to the Third Edition

    • A chapter on Bayesian decision theory, covering Bayesian and frequentist decision theory as well as the connection of empirical Bayes with James–Stein estimation
    • A chapter on the practical implementation of MCMC methods using the BUGS software
    • Greatly expanded chapter on hierarchical models that shows how this area is well suited to the Bayesian paradigm
    • Many new applications from a variety of social science disciplines
    • Double the number of exercises, with 20 now in each chapter
    • Updated BaM package in R, including new datasets, code, and procedures for calling BUGS packages from R

    This bestselling, highly praised text continues to be suitable for a range of courses, including an introductory course or a computing-centered course. It shows students in the social and behavioral sciences how to use Bayesian methods in practice, preparing them for sophisticated, real-world work in the field.

    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

    Bayesian Decision Theory
    Introducing Decision Theory
    Basic Definitions
    Regression-Style Models with Decision Theory
    James-Stein Estimation
    Empirical Bayes
    Exercises

    Monte Carlo and Related Iterative 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: R Code 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

    Implementing Bayesian Models with Markov Chain Monte Carlo
    Introduction to Bayesian Software Solutions
    It’s Only a Name: BUGS
    Model Specification with BUGS
    Differences between WinBUGS and JAGS Code
    Technical Background about the Algorithm
    Epilogue
    Exercises

    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

    Markov Chain Monte Carlo Extensions
    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

    REFERENCES

    AUTHOR INDEX
    SUBJECT INDEX

    Biography

    Jeff Gill is a professor in the Department of Political Science, the Division of Biostatistics, and the Department of Surgery (Public Health Sciences) at Washington University. He is the author of several books and has published numerous research articles. His research applies Bayesian modeling and data analysis to questions in general social science quantitative methodology, political behavior and institutions, and medical/health data analysis using computationally intensive tools. He received his B.A. from UCLA, MBA from Georgetown University, Ph.D. from American University, and Post-Doctorate from Harvard University.

    Praise for the Third Edition:
    Bayesian Methods covers a broad yet essential scope of topics necessary for one to understand and conduct applied Bayesian analysis. The numerous social science examples should resonate with the target audience, and the availability of the code and data in an R package, BaM, further enhances the appeal of the book.
    The American Statistician, 2016

    Praise for the Second Edition:
    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.
    —S.V. Subramanian, Harvard School of Public Health

    One of the 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