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## Details

Document Type: | Book |
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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. |

## Reviews

*Editorial reviews*

Publisher Synopsis

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 MCMC issues ...-Michael Smithson, Journal of Educational and Behavioral Statistics, June 2010The book will be very suitable for students of social science ... The reference list is carefully compiled; it will be very useful for a well-motivated reader. Altogether it is a very readable book, based on solid scholarship and written with conviction, gusto, and a sense of fun.-International Statistical Review (2009), 77, 2The second edition of Bayesian Methods: A Social and Behavioral Sciences Approach is a major update from the original version. ... The result is a general audience text suitable for a first course in Bayesian statistics at the upper undergraduate level for highly quantitative students or at the graduate level for students in a wider variety of fields. ... Of the texts I have tried so far in [my] class, Gill's book has definitely worked the best for me. ... this book fills an important market segment for classes where the canonical Bayesian texts are a bit too advanced. The emphasis is on using Bayesian methods in practice, with topics introduced via higher-level discussions followed by implementation and theory. ...-Herbert K.H. Lee, University of California, Santa Cruz, The American Statistician, November 2008Praise for the First Edition:This book is a brilliant and importantly very accessible introduction to the concept and application of Bayesian approaches to data analysis. The clear strength of the book is in making the concept practical and accessible, without necessarily dumbing it down. ... The coverage is also remarkable.-Dr. S.V. Subramanian, Harvard School of Public Health, Cambridge, Massachusetts, USAOne of the signal contributions of Bayesian Methods: A Social and Behavioral Sciences Approach is to reintroduce Bayesian inference and computing to a general social sciences audience. This is an important contribution-one that will make demand for this book high ... Jeff Gill has gone some way toward reinventing the graduate-level methodology textbook ... Gill's treatment of the practicalities of convergence is a real service ... new users of the technique will appreciate this material. ... the inclusion of material on hierarchical modeling at first seems unconventional; its use in political science, while increasing, has been limited. However, Bayesian inference and MCMC methods are well-suited to these types of problems, and it is exactly these types of treatments that push the discipline in new directions. As noted, a number of monographs have appeared recently to reintroduce Bayesian inference to a new generation of computer-savvy statisticians. ... However, Gill achieves what these do not: a quality introduction and reference guide to Bayesian inference and MCMC methods that will become a standard in political methodology.-The Journal of Politics, November 2003 Read more...

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