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Bayesian Methods

A Social and Behavioral Sciences Approach, Third Edition

By Jeff Gill

Chapman and Hall/CRC – 2014 – 724 pages

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

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    978-1-43-986248-3
    December 11th 2014

Description

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.

Reviews

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

Contents

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

Author Bio

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.

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