Bayesian Methods
Chapman & Hall/CRC (Verlag)
978-1-58488-562-7 (ISBN)
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The first edition of Bayesian Methods: A Social and Behavioral Sciences Approach helped pave the way for Bayesian approaches to become more prominent in social science methodology. While the focus remains on practical modeling and basic theory as well as on intuitive explanations and derivations without skipping steps, this second edition incorporates the latest methodology and recent changes in software offerings.
New to the Second Edition
Two chapters on Markov chain Monte Carlo (MCMC) that cover ergodicity, convergence, mixing, simulated annealing, reversible jump MCMC, and coupling
Expanded coverage of Bayesian linear and hierarchical models
More technical and philosophical details on prior distributions
A dedicated R package (BaM) with data and code for the examples as well as a set of functions for practical purposes such as calculating highest posterior density (HPD) intervals
Requiring only a basic working knowledge of linear algebra and calculus, this text is one of the few to offer a graduate-level introduction to Bayesian statistics for social scientists. It first introduces Bayesian statistics and inference, before moving on to assess model quality and fit. Subsequent chapters examine hierarchical models within a Bayesian context and explore MCMC techniques and other numerical methods. Concentrating on practical computing issues, the author includes specific details for Bayesian model building and testing and uses the R and BUGS software for examples and exercises.
Jeff Gill, University of California - Davis, USA, DAVIS CA, U.S.A
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
| Erscheint lt. Verlag | 26.11.2007 |
|---|---|
| Reihe/Serie | Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences |
| Zusatzinfo | 69 Tables, black and white; 47 Illustrations, black and white |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 1179 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| ISBN-10 | 1-58488-562-9 / 1584885629 |
| ISBN-13 | 978-1-58488-562-7 / 9781584885627 |
| Zustand | Neuware |
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