Bayesian Methods A Social and Behavioral Sciences Approach, Third Edition

An Update of the Most Popular Graduate-Level Introductions to Bayesian Statistics for Social Scientists Now that Bayesian modeling has become standard, MCMC is well understood and trusted, and computing power continues to increase, Bayesian Methods: A Social and Behavioral Sciences Approach, Third Edition focuses more on implementation details of the procedures and less on justifying procedures. The expanded examples reflect this updated approach. New to the Third Edition A chapter on Bayesian decision theory, covering Bayesian and frequentist decision theory as well as the connection of empirical Bayes with James–Stein estimation A chapter on the practical implementation of MCMC methods using the BUGS software Greatly expanded chapter on hierarchical models that shows how this area is well suited to the Bayesian paradigm Many new applications from a variety of social science disciplines Double the number of exercises, with 20 now in each chapter Updated BaM package in R, including new datasets, code, and procedures for calling BUGS packages from R This bestselling, highly praised text continues to be suitable for a range of courses, including an introductory course or a computing-centered course. It shows students in the social and behavioral sciences how to use Bayesian methods in practice, preparing them for sophisticated, real-world work in the field.

BACKGROUND AND INTRODUCTION IntroductionMotivation and Justification Why Are We Uncertain about Probability?Bayes' Law Conditional Inference with Bayes' Law Historical Comments The Scientific Process in Our Social Sciences Introducing Markov Chain Monte Carlo Techniques ExercisesSPECIFYING BAYESIAN MODELS Purpose Likelihood Theory and Estimation The Basic Bayesian FrameworkBayesian "Learning" Comments on Prior Distributions Bayesian versus Non-Bayesian Approaches ExercisesComputational Addendum: R for Basic AnalysisTHE NORMAL AND STUDENT'S-T MODELS Why Be Normal? The Normal Model with Variance Known The Normal Model with Mean Known The Normal Model with Both Mean and Variance Unknown Multivariate Normal Model, µ and S Both Unknown Simulated Effects of Differing Priors Some Normal Comments The Student's t Model Normal Mixture Models Exercises Computational Addendum: Normal ExamplesTHE BAYESIAN LINEAR MODEL The Basic Regression ModelPosterior Predictive Distribution for the Data The Bayesian Linear Regression Model with HeteroscedasticityExercises Computational AddendumTHE BAYESIAN PRIOR A Prior Discussion of Priors A Plethora of Priors Conjugate Prior FormsUninformative Prior DistributionsInformative Prior DistributionsHybrid Prior FormsNonparametric Priors Bayesian Shrinkage ExercisesASSESSING MODEL QUALITY MotivationBasic Sensitivity AnalysisRobustness EvaluationComparing Data to the Posterior Predictive Distribution Simple Bayesian Model Averaging Concluding Comments on Model Quality Exercises Computational AddendumBAYESIAN HYPOTHESIS TESTING AND THE BAYES' FACTOR Motivation Bayesian Inference and Hypothesis TestingThe Bayes' Factor as EvidenceThe Bayesian Information Criterion (BIC) The Deviance Information Criterion (DIC)Comparing Posteriors with the Kullback-Leibler DistanceLaplace Approximation of Bayesian Posterior Densities Exercises Bayesian Decision Theory Introducing Decision Theory Basic Definitions Regression-Style Models with Decision Theory James-Stein Estimation Empirical Bayes Exercises Monte Carlo and Related Iterative MethodsBackground Basic Monte Carlo Integration Rejection Sampling Classical Numerical Integration Gaussian Quadrature Importance Sampling/Sampling Importance ResamplingMode Finding and the EM AlgorithmSurvey of Random Number Generation Concluding Remarks Exercises Computational Addendum: R Codefor Importance SamplingBASICS OF MARKOV CHAIN MONTE CARLO Who Is Markov and What Is He Doing with Chains?General Properties of Markov ChainsThe Gibbs SamplerThe Metropolis-Hastings AlgorithmThe Hit-and-Run AlgorithmThe Data Augmentation Algorithm Historical CommentsExercises Computational Addendum: Simple R Graphing Routines forMCMC Implementing Bayesian Models with Markov Chain Monte Carlo Introduction to Bayesian Software Solutions It’s Only a Name: BUGS Model Specification with BUGS Differences between WinBUGS and JAGS Code Technical Background about the Algorithm Epilogue Exercises BAYESIAN HIERARCHICAL MODELS Introduction to Multilevel Models Standard Multilevel Linear Models A Poisson-Gamma Hierarchical Model The General Role of Priors and Hyperpriors Exchangeability Empirical Bayes Exercises Computational Addendum: Instructions for Running JAGS, Trade Data ModelSOME MARKOV CHAIN MONTE CARLO THEORY Motivation Measure and Probability Preliminaries Specific Markov Chain PropertiesDefining and Reaching Convergence Rates of Convergence Implementation ConcernsExercisesUTILITARIAN MARKOV CHAIN MONTE CARLO Practical Considerations and AdmonitionsAssessing Convergence of Markov ChainsMixing and AccelerationProducing the Marginal Likelihood Integral from Metropolis-Hastings Output Rao-Blackwellizing for Improved Variance Estimation Exercises Computational Addendum: R Code for the Death Penalty Support Model and BUGS Code for the Military Personnel ModelMarkov Chain Monte Carlo ExtensionsSimulated Annealing Reversible Jump AlgorithmsPerfect SamplingExercisesAPPENDIX A: GENERALIZED LINEAR MODEL REVIEW Terms The Generalized Linear Model Numerical Maximum LikelihoodQuasi-Likelihood ExercisesR for Generalized Linear ModelsAPPENDIX B: COMMON PROBABILITY DISTRIBUTIONS REFERENCES AUTHOR INDEX SUBJECT INDEX

Jeff Gill is a professor in the Department of Political Science, the Division of Biostatistics, and the Department of Surgery (Public Health Sciences) at Washington University. He is the author of several books and has published numerous research articles. His research applies Bayesian modeling and data analysis to questions in general social science quantitative methodology, political behavior and institutions, and medical/health data analysis using computationally intensive tools. He received his B.A. from UCLA, MBA from Georgetown University, Ph.D. from American University, and Post-Doctorate from Harvard University.