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Bayes Linear Statistics: Theory and Methods

Bayes Linear Statistics: Theory and Methods

Michael Goldstein, David Wooff

ISBN: 978-0-470-06567-9

Apr 2007

536 pages

$148.99

Description

Bayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodology, and practicalities of this important field.

The text provides a thorough coverage of Bayes linear analysis, from the development of the basic language to the collection of algebraic results needed for efficient implementation, with detailed practical examples.

The book covers:

  • The importance of partial prior specifications for complex problems where it is difficult to supply a meaningful full prior probability specification.
  • Simple ways to use partial prior specifications to adjust beliefs, given observations.
  • Interpretative and diagnostic tools to display the implications of collections of belief statements, and to make stringent comparisons between expected and actual observations.
  • General approaches to statistical modelling based upon partial exchangeability judgements.
  • Bayes linear graphical models to represent and display partial belief specifications, organize computations, and display the results of analyses.

Bayes Linear Statistics is essential reading for all statisticians concerned with the theory and practice of Bayesian methods. There is an accompanying website hosting free software and guides to the calculations within the book.

Preface.

1 The Bayes linear approach.

2 Expectation.

3 Adjusting beliefs.

4 The observed adjustment.

5 Partial Bayes linear analysis.

6 Exchangeable beliefs.

7 Co-exchangeable beliefs.

8 Learning about population variances.

9 Belief comparison.

10 Bayes linear graphical models.

11 Matrix algebra for implementing the theory.

12 Implementing Bayes linear statistics.

A Notation.

B Index of examples.

C Software for Bayes linear computation.

C.1 [B/D].

C.2 BAYES-LIN.

References.

Index.

“The book is an essential reading for all statisticians concerned with the theory and practice of Bayesian methods. There is an accompanying website hosting free software and guides to the calculations within the book.”  (Zentralblatt MATH, 2012)

"Summarizing, the book is an interesting compendium of methods of updating beliefs." (Stat Papers, 2010)

"The authors are to be congratulated for their pioneering effort in writing this book. Hopefully, more books and articles will follow, and the methodology will someday be part of mainstream statistics." (Technometrics, November 2008)

"The authors are to be congratulated for their pioneering effort in writing this book.  Hopefully, more books and articles will follow, and the methodology will someday be part of mainstream statistics." (Technometrics, November 2008)

"The book provides an extensive introduction and explanation of the subject and augments theory with numerous illustrative examples, including relevant considerations for specifying beliefs and diagnostics for assessing appropriateness." (Journal of the American Statistical Association, September 2008)