Statistical inference : an integrated Bayesian/likelihood approach / Murray Aitkin.

Includes bibliographical references and index.

1. Theories of statistical inference --
2. The integrated Bayes/likelihood approach --
3. t-Tests and normal variance tests --
4. Unified analysis of finite populations --
5. Regression and analysis of variance --
6. Binomial and multinomial data --
7. Goodness of fit and model diagnostics --
8. Complex models.

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 inferenc.

Also available as an electronic resource.