Bayesian Analysis for the Social Sciences

by Simon Jackman (Stanford University, Palo Alto, CA )

• ISBN13: 9780470686638
• ISBN10: 0470686634
• Format: eBook
• Copyright: 2009-10-01
• Publisher: Wiley

Summary

Bayesian methods are increasingly being used in the social sciences, as the problems encountered lend themselves so naturally to the subjective qualities of Bayesian methodology. This book provides an accessible introduction to Bayesian methods, tailored specifically for social science students. It contains lots of real examples from political science, psychology, sociology, and economics, exercises in all chapters, and detailed descriptions of all the key concepts, without assuming any background in statistics beyond a first course. It features examples of how to implement the methods using WinBUGS - the most-widely used Bayesian analysis software in the world - and R - an open-source statistical software. The book is supported by a Website featuring WinBUGS and R code, data sets, and solutions to exercises.

Table of Contents

List of Figures

List of Tables

Preface

Acknowledgments

Introduction

Introducing Bayesian Analysis

The foundations of Bayesian inference

What is probability?

Subjective probability in Bayesian statistics

Bayes theorem, discrete case

Bayes theorem, continuous parameter

Parameters as random variables, beliefs as distributions

Communicating the results of a Bayesian analysis

Asymptotic properties of posterior distributions

Bayesian hypothesis testing

From subjective beliefs to parameters and models

Historical note

Getting started: Bayesian analysis for simple models

Learning about probabilities, rates and proportions

Associations between binary variables

Learning from counts

Learning about a normal mean and variance

Regression models

Further reading

Simulation Based Bayesian Analysis

Monte Carlo methods

Simulation consistency

Inference for functions of parameters

Marginalization via Monte Carlo integration

Sampling algorithms

Further reading

Markov chains

Notation and definitions

Properties of Markov chains

Convergence of Markov chains

Limit theorems for Markov chains

Further reading

Markov chain Monte Carlo

Metropolis-Hastings algorithm

Gibbs sampling

Implementing Markov chain Monte Carlo

Software for Markov chain Monte Carlo

Assessing convergence and run-length

Working with BUGS/JAGS from R

Tricks of the trade

Other examples

Further reading

Advanced Applications in the Social Sciences

Hierarchical Statistical Models

Data and parameters that vary by groups: the case for hierarchical modeling

ANOVA as a hierarchical model

Hierarchical models for longitudinal data

Hierarchical models for non-normal data

Multi-level models

Bayesian analysis of choice making

Regression models for binary responses

Ordered outcomes

Multinomial outcomes

Multinomial probit

Bayesian approaches to measurement

Bayesian inference for latent states

Factor analysis

Item-response models

Dynamic measurement models

Appendices

Working with vectors and matrices

Probability review

Foundations of probability

Probability densities and mass functions

Convergence of sequences of random variabales

Proofs of selected propositions

Products of normal densities

Conjugate analysis of normal data

Asymptotic normality of the posterior density

References

Topic index

Author index

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