Bayesian methods : a social and behavioral sciences approach

著者

書誌事項

Bayesian methods : a social and behavioral sciences approach

Jeff Gill

Chapman & Hall/CRC, c2002

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

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

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