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Statistical Inference: An Integrated Bayesian/Likelihood Approach (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)

Statistical Inference: An Integrated Bayesian/Likelihood Approach (Chapman & Hall/CRC Monographs on Statistics & Applied Probability)

By: Murray Aitkin (author)Hardback

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Description

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.

About Author

Murray Aitkin is an honorary professorial fellow in the Department of Mathematics and Statistics at the University of Melbourne in Australia.

Contents

Theories of Statistical InferenceExampleStatistical models The likelihood function TheoriesNonmodel-based repeated samplingConclusion The 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 diagnosis t-Tests and Normal Variance TestsOne-sample t-testTwo samples: equal variancesThe two-sample test Two samples: different variances The normal model varianceVariance heterogeneity test Unified 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 Discussion Regression and Analysis of VarianceMultiple regressionNonnested models Binomial 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" analysis Goodness of Fit and Model DiagnosticsFrequentist model diagnostics Bayesian model diagnostics The posterior predictive distributionMultinomial deviance computationModel comparison through posterior deviances Examples Simulation study Discussion Complex ModelsThe data augmentation algorithmTwo-level variance component modelsTest for a zero variance componentFinite mixtures References Author Index Subject Index

Product Details

  • ISBN13: 9781420093438
  • Format: Hardback
  • Number Of Pages: 254
  • ID: 9781420093438
  • weight: 568
  • ISBN10: 1420093436

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