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    Bayesian Analysis for the Social Sciences

    ISBN-10: 0470011548
    ISBN-13: 9780470011546
    Edition: 2006
    Author(s): Simon Jackman
    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,  More...
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    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: 2.794
    Language: English

    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.

    List of Figures
    List of Tables
    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
    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
    Invariant measure
    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
    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
    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
    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
    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
    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
    Topic index
    Author index

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