First Course in Bayesian Statistical Methods

2009 /E

Hoff, Peter D. 저자(글)

Springer · 2009년 06월 01일

책 소개

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 linear mixed effects models and semiparametric copula estimation. Numerous examples from the social, biological and physical sciences show how to implement these methodologies in practice.Monte Carlo summaries of posterior distributions play an important role in Bayesian data analysis. The open-source R statistical computing environment provides sufficient functionality to make Monte Carlo estimation very easy for a large number of statistical models, and example R-code is provided throughout the text. Much of the example code can be run ``as is'' in R, and essentially all of it can be run after downloading the relevant datasets from the companion website for this book.

작가정보

저자(글) Hoff, Peter D.

목차

• Introduction and examplesp. 1
  Introductionp. 1
  Why Bayes?p. 2
  Estimating the probability of a rare eventp. 3
  Building a predictive modelp. 8
  Where we are goingp. 11
  Discussion and further referencesp. 12
  Belief, probability and exchangeabilityp. 13
  Belief functions and probabilitiesp. 13
  Events, partitions and Bayes' rulep. 14
  Independencep. 17
  Random variablesp. 17
  Discrete random variablesp. 18
  Continuous random variablesp. 19
  Descriptions of distributionsp. 21
  Joint distributionsp. 23
  Independent random variablesp. 26
  Exchangeabilityp. 27
  de Finetti's theoremp. 29
  Discussion and further referencesp. 30
  One-parameter modelsp. 31
  The binomial modelp. 31
  Inference for exchangeable binary datap. 35
  Confidence regionsp. 41
  The Poisson modelp. 43
  Posterior inferencep. 45
  Example: Birth ratesp. 48
  Exponential families and conjugate priorsp. 51
  Discussion and further referencesp. 52
  Monte Carlo approximationp. 53
  The Monte Carlo methodp. 53
  Posterior inference for arbitrary functionsp. 57
  Sampling from predictive distributionsp. 60
  Posterior predictive model checkingp. 62
  Discussion and further referencesp. 65
  The normal modelp. 67
  The normal modelp. 67
  Inference for the mean, conditional on the variancep. 69
  Joint inference for the mean and variancep. 73
  Bias, variance and mean squared errorp. 79
  Prior specification based on expectationsp. 83
  The normal model for non-normal datap. 84
  Discussion and further referencesp. 86
  Posterior approximation with the Gibbs samplerp. 89
  A semiconjugate prior distributionp. 89
  Discrete approximationsp. 90
  Sampling from the conditional distributionsp. 92
  Gibbs samplingp. 93
  General properties of the Gibbs samplerp. 96
  Introduction to MCMC diagnosticsp. 98
  Discussion and further referencesp. 104
  The multivariate normal modelp. 105
  The multivariate normal densityp. 105
  A semiconjugate prior distribution for the meanp. 107
  The inverse-Wishart distributionp. 109
  Gibbs sampling of the mean and covariancep. 112
  Missing data and imputationp. 115
  Discussion and further referencesp. 123
  Group comparisons and hierarchical modelingp. 125
  Comparing two groupsp. 125
  Comparing multiple groupsp. 130
  Exchangeability and hierarchical modelsp. 131
  The hierarchical normal modelp. 132
  Posterior inferencep. 133
  Example: Math scores in U.S. public schoolsp. 135
  Prior distributions and posterior approximationp. 137
  Posterior summaries and shrinkagep. 140
  Hierarchical modeling of means and variancesp. 143
  Analysis of math score datap. 145
  Discussion and further referencesp. 146
  Linear regressionp. 149
  The linear regression modelp. 149
  Least squares estimation for the oxygen uptake datap. 153
  Bayesian estimation for a regression modelp. 154
  A semiconjugate prior distributionp. 154
  Default and weakly informative prior distributionsp. 155
  Model selectionp. 160
  Bayesian model comparisonp. 163
  Gibbs sampling and model averagingp. 167
  Discussion and further referencesp. 170
  Nonconjugate priors and Metropolis-Hastings algorithmsp. 171
  Generalized linear modelsp. 171
  The Metropolis algorithmp. 173
  The Metropolis algorithm for Poisson regressionp. 179
  Metropolis, Metropolis-Hastings and Gibbsp. 181
  The Metropolis-Hastings algorithmp. 182
  Why does the Metropolis-Hastings algorithm work?p. 184
  Combining the Metropolis and Gibbs algorithmsp. 187
  A regression model with correlated errorsp. 188
  Analysis of the ice core datap. 191
  Discussion and further referencesp. 192
  Linear and generalized linear mixed effects modelsp. 195
  A hierarchical regression modelp. 195
  Full conditional distributionsp. 198
  Posterior analysis of the math score datap. 200
  Generalized linear mixed effects modelsp. 201
  A Metropolis-Gibbs algorithm for posterior approximationp. 202
  Analysis of tumor location datap. 203
  Discussion and further referencesp. 207
  Latent variable methods for ordinal datap. 209
  Ordered probit regression and the rank likelihoodp. 209
  Probit regressionp. 211
  Transformation models and the rank likelihoodp. 214
  The Gaussian copula modelp. 217
  Rank likelihood for copula estimationp. 218
  Discussion and further referencesp. 223
  Exercisesp. 225
  Common distributionsp. 253
  Referencesp. 259
  Indexp. 267
  Table of Contents provided by Ingram. All Rights Reserved.

기본정보

ISBN	9780387922997 ( 0387922997 )
발행(출시)일자	2009년 06월 01일
쪽수	271쪽
크기	156 * 234 * 18 mm / 576 g
총권수	1권
언어	영어