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Bayes Linear Statistics, Theory & Methods

ISBN: 978-0-470-01562-9
536 pages
June 2007
Bayes Linear Statistics, Theory & Methods (0470015624) cover image
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.

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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.

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.

Bibliography.

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Michael Goldstein, Professor of Statistics, Department of Mathematical Sciences, University of Durham
Michael Goldstein has worked on and researched the Bayes linear approach for around 30 years, his general interests being in the foundations, methodology and applications of Bayesian/subjectivist approaches to statistics. He has an outstanding reputation as one of the most original thinkers in the field, and was a contributing author to Wiley’s “Encyclopedia of Statistical Sciences”.

David Wooff, Director of Statistics & Mathematics Consultancy Unit and Senior Lecturer in Statistics, Department of Mathematical Sciences, University of Durham
David Wooff has been involved in a long collaboration for over 20 years with Michael Goldstein and others on developing Bayes linear methods, his primary research interest being the general development and application of Bayes linear methodology.

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“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)

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The Bayes Linear Methods HomepageVisit the author's website for a directory of links to the Bayes community.
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