(Not in Statistical Inference
An Integrated Bayesian/Likelihood Approach
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$89.95$80.96 - Hardback: 254 pages
- Also available in e-Book
- Published: June 2010
- ISBN: 978-1-4200934-3-8
- Publisher: Chapman & Hall
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- By Murray Aitkin.
- Series Edited by Richard L. Smith, Valerie Isham, Thomas A. Louis, Jianqing Fan, Howell Tong, Niels Keiding and Susan.A Murphy.
Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability.
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.
Table of Contents
Theories of Statistical Inference
Example
Statistical models
The likelihood function
Theories
Nonmodel-based repeated sampling
Conclusion
The Integrated Bayes/Likelihood Approach
Introduction
Probability
Prior ignorance
The importance of parametrization
The simple/simple hypothesis testing problem
The simple/composite hypothesis testing problem
Posterior likelihood approach
Bayes factors
The comparison of unrelated models
Example—GHQ score and psychiatric diagnosis
t-Tests and Normal Variance Tests
One-sample t-test
Two samples: equal variances
The two-sample test
Two samples: different variances
The normal model variance
Variance heterogeneity test
Unified Analysis of Finite Populations
Sample selection indicators
The Bayesian bootstrap
Sampling without replacement
Regression models
More general regression models
The multinomial model for multiple populations
Complex sample designs
A complex example
Discussion
Regression and Analysis of Variance
Multiple regression
Nonnested models
Binomial and Multinomial Data
Single binomial samples
Single multinomial samples
Two-way tables for correlated proportions
Multiple binomial samples
Two-way tables for categorical responses—no fixed margins
Two-way tables for categorical responses—one fixed margin
Multinomial "nonparametric" analysis
Goodness of Fit and Model Diagnostics
Frequentist model diagnostics
Bayesian model diagnostics
The posterior predictive distribution
Multinomial deviance computation
Model comparison through posterior deviances
Examples
Simulation study
Discussion
Complex Models
The data augmentation algorithm
Two-level variance component models
Test for a zero variance component
Finite mixtures
References
Author Index
Subject Index
Author Biography
Murray Aitkin is an honorary professorial fellow in the Department of Mathematics and Statistics at the University of Melbourne in Australia.
