Description
Taylor & Francis Ltd Statistical Inference 2010 Edition by Murray Aitkin
Filling a gap in current Bayesian theory, Statistical Inference: An Integrated Bayesian/Likelihood Approach presents a unified Bayesian treatment of parameter inference and model comparisons that can be used with simple diffuse prior specifications. This novel approach provides new solutions to difficult model comparison problems and offers direct Bayesian counterparts of frequentist t-tests and other standard statistical methods for hypothesis testing.After an overview of the competing theories of statistical inference, the book introduces the Bayes/likelihood approach used throughout. It presents Bayesian versions of one- and two-sample t-tests, along with the corresponding normal variance tests. The author then thoroughly discusses the use of the multinomial model and noninformative Dirichlet priors in "model-free" or nonparametric Bayesian survey analysis, before covering normal regression and analysis of variance. In the chapter on binomial and multinomial data, he gives alternatives, based on Bayesian analyses, to current frequentist nonparametric methods. The text concludes with new goodness-of-fit methods for assessing parametric models and a discussion of two-level variance component models and finite mixtures.Emphasizing the principles of Bayesian inference and Bayesian model comparison, this book develops a unique methodology for solving challenging inference problems. It also includes a concise review of the various approaches to inference. Theories of Statistical InferenceExampleStatistical models The likelihood function TheoriesNonmodel-based repeated samplingConclusionThe Integrated Bayes/Likelihood ApproachIntroductionProbability Prior ignorance The importance of parametrizationThe simple/simple hypothesis testing problemThe simple/composite hypothesis testing problemPosterior likelihood approachBayes factors The comparison of unrelated models Example-GHQ score and psychiatric diagnosist-Tests and Normal Variance TestsOne-sample t-testTwo samples: equal variancesThe two-sample test Two samples: different variances The normal model varianceVariance heterogeneity testUnified Analysis of Finite PopulationsSample selection indicators The Bayesian bootstrapSampling without replacement Regression modelsMore general regression models The multinomial model for multiple populations Complex sample designsA complex example DiscussionRegression and Analysis of VarianceMultiple regressionNonnested modelsBinomial and Multinomial DataSingle binomial samples Single multinomial samples Two-way tables for correlated proportions Multiple binomial samples Two-way tables for categorical responses-no fixed marginsTwo-way tables for categorical responses-one fixed margin Multinomial "nonparametric" analysisGoodness of Fit and Model DiagnosticsFrequentist model diagnostics Bayesian model diagnostics The posterior predictive distributionMultinomial deviance computationModel comparison through posterior deviances Examples Simulation study DiscussionComplex ModelsThe data augmentation algorithmTwo-level variance component modelsTest for a zero variance componentFinite mixturesReferencesAuthor Index Subject Index