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Bayesian Methods

A Social and Behavioral Sciences Approach

By Jeff Gill

Chapman and Hall/CRC – 2002 – 480 pages

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

Purchasing Options:

  • Hardback:
    978-1-58488-288-6
    May 29th 2002
    Out-of-print

Description

Despite increasing interest in Bayesian approaches, especially across the social sciences, it has been virtually impossible to find a text that introduces Bayesian data analysis in a manner accessible to social science students. The Bayesian paradigm is ideally suited to the type of data analysis they will have to perform, but the associated mathematics can be daunting.

Bayesian Methods: A Social and Behavioral Sciences Approach presents the basic principles of Bayesian statistics in a treatment designed specifically for students in the social sciences and related fields. Requiring few prerequisites, it first introduces Bayesian statistics and inference with detailed descriptions of setting up a probability model, specifying prior distributions, calculating a posterior distribution, and describing the results. This is followed by explicit guidance on assessing model quality and model fit using various diagnostic techniques and empirical summaries. Finally, it introduces hierarchical models within the Bayesian context, which leads naturally to Markov Chain Monte Carlo computing techniques and other numerical methods.

The author emphasizes practical computing issues, includes specific details for Bayesian model building and testing, and uses the freely available R and BUGS software for examples and exercise problems. The result is an eminently practical text that is comprehensive, rigorous, and ideally suited to teaching future empirical social scientists.

Reviews

"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

"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

BACKGROUND AND INTRODUCTION

Introduction

Motivation and Justification

Why Are We Uncertain about Probability

Bayes Law

Bayes Law and Conditional Inference

Historical Comments

The Scientific Process in Our Social Sciences

LIKELIHOOD INFERENCE AND THE GENERALIZED LINEAR MODEL

Motivation

Likelihood Theory and Estimation

The Generalized Linear Model

Numerical Maximum Likelihood

Advanced Topics

THE BAYESIAN SETUP

The Basic Framework

Context and Controversy

Rivals for Power

Example: The Timing of Polls

THE NORMAL AND STUDENT'S-T MODELS

Why Be Normal

The Normal Model with Variance Known

The Normal Model with Mean Known

Multivariate Normal Model When m and S Are Both Unknown

Final Normal Comments

The Students-t Model

Advanced Topics

THE BAYESIAN PRIOR

A Prior Discussion of Priors

A Plethora of Priors

ASSESSING MODEL QUALITY

Motivation

The Bayesian Linear Regression Model

Example: The 2000 US Election in Palm Beach County

Sensitivity Analysis

Robustness Evaluation

Comparing Data to the Posterior Predictive Distribution

Concluding Remarks

Advanced Topics

BAYESIAN HYPOTHESIS TESTING AND THE BAYES FACTOR

Motivation

Bayesian Inference and Hypothesis Testing

The Bayes Factor as Evidence

The Bayesian Information Criterion

Things about the Bayes Factor That Do Not Work

Concluding Remarks

Advanced Topics

BAYESIAN POSTERIOR SIMULATION

Background

Basic Monte Carlo Integration

Rejection Sampling

Classical Numerical Integration

Importance Sampling/Sampling Importance Resampling

Mode Finding and the EM Algorithm

Concluding Remarks

Advanced Topics

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

Data Augmentation

Practical Considerations and Admonitions

Historical Comments

BAYESIAN HIERARCHICAL MODELS

Introduction to Hierarchical Models

A Poisson-Gamma Hierarchical Model

The Role of Priors and Hyperpriors

Specifying Hierarchical Models

Exchangeability

Computational Issues

Advanced Topics

PRACTICAL MARKOV CHAIN MONTE CARLO

The Problem of Assessing Convergence

Model Checking and Assessment

Improving Mixing and Convergence

Hybrid Markov Chains

Answers to the Really Practical Questions

Advanced Topics

Each chapter also contains References and Exercises

Name: Bayesian Methods: A Social and Behavioral Sciences Approach (eBook)Chapman and Hall/CRC 
Description: By Jeff Gill. Despite increasing interest in Bayesian approaches, especially across the social sciences, it has been virtually impossible to find a text that introduces Bayesian data analysis in a manner accessible to social science students. The Bayesian paradigm is...
Categories: Quantitative Methods, Statistical Theory & Methods, Statistics for the Biological Sciences