Statistical Inference: An Integrated Bayesian/Likelihood Approach

Murray Aitkin

June 2, 2010 by Chapman and Hall/CRC
Reference - 254 Pages - 95 B/W Illustrations
ISBN 9781420093438 - CAT# C3436
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability

USD$114.95

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Features

  • Provides new, straightforward solutions for comparing statistical models
  • Offers a unified approach to all model comparison problems that avoids difficulties of Bayes factors and p-values by employing the full posterior distribution of the likelihood
  • Explains how improper, diffuse, and noninformative priors are used for both parameter inference and model comparison
  • Presents a general alternative to the design-based approach for finite population inference using a simple multinomial model and Dirichlet priors
  • Discusses how to identify the best model via the stochastic ordering of deviance distributions

Summary

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.