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Bayesian Methods

A Social and Behavioral Sciences Approach, Second Edition

By Jeff Gill

Chapman and Hall/CRC – 2007 – 752 pages

Series: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences

Purchasing Options:

  • Add to CartHardback: $89.95
    978-1-58488-562-7
    November 26th 2007

Description

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.

  • Reviews

    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

    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

    Name: Bayesian Methods: A Social and Behavioral Sciences Approach, Second Edition (Hardback)Chapman and Hall/CRC 
    Description: By Jeff Gill. 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...
    Categories: Regression Analysis and Multivariate Statistics, Statistical Theory & Methods, Statistics for the Biological Sciences