Statistical Inference An Integrated Bayesian/Likelihood Approach
Auteur : Aitkin Murray
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 Inference. The Integrated Bayes/Likelihood Approach. t-Tests and Normal Variance Tests. Unified Analysis of Finite Populations. Regression and Analysis of Variance. Binomial and Multinomial Data. Goodness of Fit and Model Diagnostics. Complex Models. References. Indices.
Murray Aitkin is an honorary professorial fellow in the Department of Mathematics and Statistics at the University of Melbourne in Australia.
Date de parution : 06-2010
15.6x23.4 cm
Date de parution : 09-2019
15.6x23.4 cm
Thème de Statistical Inference :
Mots-clés :
Posterior Distribution; Credible Interval; posterior; Bayes Factors; distribution; Deviance Difference; credible; Central Credible Interval; interval; Null Hypothesis; bayes; FBF; factor; Deviance Distribution; deviance; Nuisance Parameters; difference; Variance Component Ratio; central; Equal Prior Probabilities; intervals; Posterior Mass Function; Integrated Likelihood; Bayesian Bootstrap; Galaxy Data; Posterior Predictive Distribution; Likelihood Ratio; IBF; Flat Prior; GHQ Score; Empirical Cdf; Cumulative Distribution Function; Profile Likelihood; Jeffreys Prior; Empirical Likelihood