Book: Statistical Inference

(CRC Press: Boca Raton, FL) -- Filling a gap in current Bayesian theory, Murray Aitkin’s  Statistical Inference: An Integrated Bayesian/Likelihood Approach (CRC Press, 2010) 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. Author, Murray Aitkin, 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.

Key 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   

 

Aitkin is an honorary professorial fellow in the Department of Mathematics and Statistics at the University of Melbourne, Australia. He co-authored the book, Statistical Modelling in GLIM4, Second Edition (OUP Oxford, 2005), part of the Oxford Statistical Science Series, and Statistical Modelling in R (Oxford University Press USA, 2009).

Aitkin has a doctorate degree in mathematical statistics from Sydney University and did postdoctoral work at the Thurstone Psychometric Laboratory at Chapel Hill, North Carolina. After a period in the Department of Statistics at the University of New South Wales, he joined the School of Behavioural Sciences at Macquarie University in 1969 and built up a small statistical consulting group there in psychology. He is currently working on two new books. Murray is a member of the International Statistical Institute (1982) and a fellow of the American Statistical Association (1984).

About The Author