Bayesian methods : a social and behavioral sciences approach /: a social and behavioral sciences approach. (2007)

• Record Type: Book
• Further Information: Note: Jeff Gill.
• Other Names: Gill, Jeff
• Contents: PREFACES; ; BACKGROUND AND INTRODUCTION; Introduction; Motivation 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; Exercises; ; SPECIFYING BAYESIAN MODELS; Purpose; Likelihood Theory and Estimation; The Basic Bayesian Framework; Bayesian "Learning"; Comments on Prior Distributions; Bayesian versus Non-Bayesian Approaches; Exercises; Computational Addendum: R for Basic Analysis; ; THE 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 Examples; ; THE BAYESIAN LINEAR MODEL; The Basic Regression Model; Posterior Predictive Distribution for the Data; The Bayesian Linear Regression Model with Heteroscedasticity; Exercises; Computational Addendum; ; THE BAYESIAN PRIOR; A Prior Discussion of Priors; A Plethora of Priors; Conjugate Prior Forms; Uninformative Prior Distributions; Informative Prior Distributions; Hybrid Prior Forms; Nonparametric Priors; Bayesian Shrinkage; Exercises; ; ASSESSING MODEL QUALITY; Motivation; Basic Sensitivity Analysis; Robustness Evaluation; Comparing Data to the Posterior Predictive Distribution; Simple Bayesian Model Averaging; Concluding Comments on Model Quality; Exercises; Computational Addendum; ; BAYESIAN HYPOTHESIS TESTING AND THE BAYES' FACTOR; Motivation; Bayesian Inference and Hypothesis Testing; The Bayes' Factor as Evidence; The Bayesian Information Criterion (BIC); The Deviance Information Criterion (DIC); Comparing Posteriors with the Kullback-Leibler Distance; Laplace Approximation of Bayesian Posterior Densities; Exercises; ; MONTE CARLO METHODS; Background; Basic Monte Carlo Integration; Rejection Sampling; Classical Numerical Integration; Gaussian Quadrature; Importance Sampling/Sampling Importance Resampling; Mode Finding and the EM Algorithm; Survey of Random Number Generation; Concluding Remarks; Exercises; Computational Addendum: RR@R for Importance Sampling; ; 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; The Hit-and-Run Algorithm; The Data Augmentation Algorithm; Historical Comments; Exercises; Computational Addendum: Simple R Graphing Routines for; MCMC; ; 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 Model; ; SOME MARKOV CHAIN MONTE CARLO THEORY; Motivation; Measure and Probability Preliminaries; Specific Markov Chain Properties; Defining and Reaching Convergence; Rates of Convergence; Implementation Concerns; Exercises; ; UTILITARIAN MARKOV CHAIN MONTE CARLO; Practical Considerations and Admonitions; Assessing Convergence of Markov Chains; Mixing and Acceleration; Producing 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 Model; ; ADVANCED MARKOV CHAIN MONTE CARLO; Simulated Annealing; Reversible Jump Algorithms; Perfect Sampling; Exercises; ; APPENDIX A: GENERALIZED LINEAR MODEL REVIEW; Terms; The Generalized Linear Model; Numerical Maximum Likelihood; Quasi-Likelihood; Exercises; R for Generalized Linear Models; ; APPENDIX B: COMMON PROBABILITY DISTRIBUTIONS; ; APPENDIX C: INTRODUCTION TO THE BUGS LANGUAGE; General Process; Technical Background on the Algorithm; WinBUGS Features; JAGS Programming; ; REFERENCES; ; AUTHOR INDEX; SUBJECT INDEX
• Edition: 2nd ed
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2007
• Extent: 1 online resource, illustrations
• Subjects: 519.542; Bayesian statistical decision theory; Social sciences -- Statistical methods
• Languages: English
• ISBNs: 9781420010824; 1420010824
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.