Statistical Inference
An Integrated Bayesian/Likelihood Approach
Seiten
2010
Chapman & Hall/CRC (Verlag)
978-1-4200-9343-8 (ISBN)
Chapman & Hall/CRC (Verlag)
978-1-4200-9343-8 (ISBN)
Sets out an integrated approach to statistical inference using the likelihood function as the primary measure of evidence for statistical model parameters, and for the statistical models themselves. This book provides both an alternative to standard Bayesian inference and the foundation for a course sequence in modern Bayesian theory.
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.
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.
Murray Aitkin is an honorary professorial fellow in the Department of Mathematics and Statistics at the University of Melbourne in Australia.
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.
| Erscheint lt. Verlag | 11.6.2010 |
|---|---|
| Zusatzinfo | 30 Tables, black and white; 95 Illustrations, black and white |
| Sprache | englisch |
| Maße | 156 x 234 mm |
| Gewicht | 630 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Statistik |
| ISBN-10 | 1-4200-9343-6 / 1420093436 |
| ISBN-13 | 978-1-4200-9343-8 / 9781420093438 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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