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Bayesian methods : a social and behavioral sciences approach

Author: Jeff Gill
Publisher: Boca Raton, Fla : Chapman & Hall/CRC, 2009.
Series: Statistics in the social and behavioral sciences series
Edition/Format:   Print book : English : 2nd ed., 3. printView all editions and formats

Requiring only a background in introductory statistics, calculus and matrix algebra, this text provides explanations of derivations and theories using a computationally oriented approach. It covers  Read more...


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Document Type: Book
All Authors / Contributors: Jeff Gill
ISBN: 9781584885627 1584885629
OCLC Number: 752356427
Description: 711 Seiten : Illustrationen.
Contents: PREFACESBACKGROUND 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, 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 ExercisesMONTE CARLO METHODS Background 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: RR@R for 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 forMCMCBAYESIAN 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 ModelADVANCED MARKOV CHAIN MONTE CARLO Simulated 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 APPENDIX C: INTRODUCTION TO THE BUGS LANGUAGE General Process Technical Background on the Algorithm WinBUGS Features JAGS Programming REFERENCES AUTHOR INDEX SUBJECT INDEX
Series Title: Statistics in the social and behavioral sciences series
Responsibility: Jeff Gill.


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Autodidacts with the requisite background in calculus, statistics, and linear algebra probably would get the greatest benefit out of Gill [due to] breadth of relevant topics and in-depth coverage of Read more...

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