Bayesian Analysis for the Social Sciences

ISBN-10: 0470011548

ISBN-13: 9780470011546

Edition: 2006

Authors: Simon Jackman

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Description:

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.
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Book details

List price: $93.00
Copyright year: 2006
Publisher: John Wiley & Sons, Incorporated
Publication date: 12/2/2009
Binding: Hardcover
Pages: 598
Size: 6.75" wide x 10.25" long x 1.25" tall
Weight: 2.816
Language: English

List of Figures
List of Tables
Preface
Acknowledgments
Introduction
Introducing Bayesian Analysis
The foundations of Bayesian inference
What is probability?
Probability in classical statistics
Subjective probability1
Subjective probability in Bayesian statistics
Bayes theorem, discrete case
Bayes theorem, continuous parameter
Conjugate priors
Bayesian updating with irregular priors
Cromwell's Rule
Bayesian updating as information accumulation
Parameters as random variables, beliefs as distributions
Communicating the results of a Bayesian analysis
Bayesian point estimation
Credible regions
Asymptotic properties of posterior distributions
Bayesian hypothesis testing
Model choice
Bayes factors
From subjective beliefs to parameters and models
Exchangeability
Implications and extensions of de Finetti's Representation Theorem
Finite exchangeability
Exchangeability and prediction
Conditional exchangeability and multiparameter models
Exchangeability of parameters: hierarchical modeling
Historical note
Getting started: Bayesian analysis for simple models
Learning about probabilities, rates and proportions
Conjugate priors for probabilities, rates and proportions
Bayes estimates as weighted averages of priors and data
Parameterizations and priors
The variance of the posterior density
Associations between binary variables
Learning from counts
Predictive inference with count data
Learning about a normal mean and variance
Variance known
Mean and variance unknown
Conditionally conjugate prior
An improper, reference prior
Conflict between likelihood and prior
Non-conjugate priors
Regression models
Bayesian regression analysis
Likelihood function
Conjugate prior
Improper, reference prior
Further reading
Simulation Based Bayesian Analysis
Monte Carlo methods
Simulation consistency
Inference for functions of parameters
Marginalization via Monte Carlo integration
Sampling algorithms
Inverse-CDF method
Importance sampling
Accept-reject sampling
Adaptive rejection sampling
Further reading
Markov chains
Notation and definitions
State space
Transition kernel
Properties of Markov chains
Existence of a stationary distribution, discrete case
Existence of a stationary distribution, continuous case
Irreducibility
Recurrence
Invariant measure
Reversibility
Aperiodicity
Convergence of Markov chains
Speed of convergence
Limit theorems for Markov chains
Simulation inefficiency
Central limit theorems for Markov chains
Further reading
Markov chain Monte Carlo
Metropolis-Hastings algorithm
Theory for the Metropolis-Hastings algorithm
Choosing the proposal density
Gibbs sampling
Theory for the Gibbs sampler
Connection to the Metropolis algorithm
Deriving conditional densities for the Gibbs sampler: statistical models as conditional independence graphs
Pathologies
Data augmentation
Missing data problems
The slice sampler
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
Thinning
Blocking
Reparameterization
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
Exchangeable parameters generate hierarchical models
�Borrowing strength� via exchangeability
Hierarchical modeling as a 'semi-pooling� estimator
Hierarchical modeling as a 'shrinkage� estimator
Computation via Markov chain Monte Carlo
ANOVA as a hierarchical model
One-way analysis of variance
Two-way ANOVA
Hierarchical models for longitudinal data
Hierarchical models for non-normal data
Multi-level models
Bayesian analysis of choice making
Regression models for binary responses
Probit model via data augmentation
Probit model via marginal data augmentation
Logit model
Binomial model for grouped binary data
Ordered outcomes
Identification
Multinomial outcomes
Multinomial logit (MNL)
Independence of irrelevant alternatives
Multinomial probit
Bayesian analysis via MCMC
Bayesian approaches to measurement
Bayesian inference for latent states
A formal role for prior information
Inference for many parameters
Factor analysis
Likelihood and prior densities
Identification
Posterior density
Inference over rank orderings of the latent variable
Incorporating additional information via hierarchical modeling
Item-response models
Dynamic measurement models
State-space models for [pooling the polls]
Bayesian inference
Appendices
Working with vectors and matrices
Probability review
Foundations of probability
Probability densities and mass functions
Probability mass functions for discrete random quantities
Probability density functions for continuous random quantities
Convergence of sequences of random variables
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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