First Course in Bayesian Statistical Methods

Name: First Course in Bayesian Statistical Methods
Availability: InStock
ISBN: 9780387922997

ISBN-10: 0387922997

ISBN-13: 9780387922997

Edition: 2009

Authors: Peter D. Hoff

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Description:

This book provides a compact self-contained introduction to the theory and application of Bayesian statistical methods. The book is accessible to readers with only a basic familiarity with probability, yet allows more advanced readers to quickly grasp the principles underlying Bayesian theory and methods. The examples and computer code allow the reader to understand and implement basic Bayesian data analyses using standard statistical models and to extend the standard models to specialized data analysis situations. The book begins with fundamental notions such as probability, exchangeability and Bayes' rule, and ends with modern topics such as variable selection in regression, generalized…

Book details

Copyright year: 2009
Publisher: Springer New York
Publication date: 6/15/2009
Binding: Hardcover
Pages: 271
Size: 6.10" wide x 9.25" long x 0.75" tall
Weight: 1.496
Language: English




Introduction and examples



Introduction



Why Bayes?



Estimating the probability of a rare event



Building a predictive model



Where we are going



Discussion and further references



Belief, probability and exchangeability



Belief functions and probabilities



Events, partitions and Bayes' rule



Independence



Random variables



Discrete random variables



Continuous random variables



Descriptions of distributions



Joint distributions



Independent random variables



Exchangeability



de Finetti's theorem



Discussion and further references



One-parameter models



The binomial model



Inference for exchangeable binary data



Confidence regions



The Poisson model



Posterior inference



Example: Birth rates



Exponential families and conjugate priors



Discussion and further references



Monte Carlo approximation



The Monte Carlo method



Posterior inference for arbitrary functions



Sampling from predictive distributions



Posterior predictive model checking



Discussion and further references



The normal model



The normal model



Inference for the mean, conditional on the variance



Joint inference for the mean and variance



Bias, variance and mean squared error



Prior specification based on expectations



The normal model for non-normal data



Discussion and further references



Posterior approximation with the Gibbs sampler



A semiconjugate prior distribution



Discrete approximations



Sampling from the conditional distributions



Gibbs sampling



General properties of the Gibbs sampler



Introduction to MCMC diagnostics



Discussion and further references



The multivariate normal model



The multivariate normal density



A semiconjugate prior distribution for the mean



The inverse-Wishart distribution



Gibbs sampling of the mean and covariance



Missing data and imputation



Discussion and further references



Group comparisons and hierarchical modeling



Comparing two groups



Comparing multiple groups



Exchangeability and hierarchical models



The hierarchical normal model



Posterior inference



Example: Math scores in U.S. public schools



Prior distributions and posterior approximation



Posterior summaries and shrinkage



Hierarchical modeling of means and variances



Analysis of math score data



Discussion and further references



Linear regression



The linear regression model



Least squares estimation for the oxygen uptake data



Bayesian estimation for a regression model



A semiconjugate prior distribution



Default and weakly informative prior distributions



Model selection



Bayesian model comparison



Gibbs sampling and model averaging



Discussion and further references



Nonconjugate priors and Metropolis-Hastings algorithms



Generalized linear models



The Metropolis algorithm



The Metropolis algorithm for Poisson regression



Metropolis, Metropolis-Hastings and Gibbs



The Metropolis-Hastings algorithm



Why does the Metropolis-Hastings algorithm work?



Combining the Metropolis and Gibbs algorithms



A regression model with correlated errors



Analysis of the ice core data



Discussion and further references



Linear and generalized linear mixed effects models



A hierarchical regression model



Full conditional distributions



Posterior analysis of the math score data



Generalized linear mixed effects models



A Metropolis-Gibbs algorithm for posterior approximation



Analysis of tumor location data



Discussion and further references



Latent variable methods for ordinal data



Ordered probit regression and the rank likelihood



Probit regression



Transformation models and the rank likelihood



The Gaussian copula model



Rank likelihood for copula estimation



Discussion and further references


Exercises


Common distributions


References


Index