# Bayes Linear Statistics, Theory and Methods

John Wiley & Sons, Apr 30, 2007 - Mathematics - 536 pages
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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### Contents

 1 The Bayes linear approach 1 2 Expectation 33 3 Adjusting beliefs 55 4 The observed adjustment 95 5 Partial Bayes linear analysis 125 6 Exchangeable beliefs 177 7 Coexchangeable beliefs 233 8 Learning about population variances 265
 10 Bayes linear graphical models 355 11 Matrix algebra for implementing the theory 431 12 Implementing Bayes linear statistics 451 A Notation 487 B Index of examples 491 C Software for Bayes linear computation 495 References 497 Index 503

 9 Belief comparison 293