Bayesian Methods
A Social and Behavioral Sciences Approach
By Jeff Gill
Published May 29th 2002 by Chapman and Hall/CRC – 480 pages
Series: Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences
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