# Bayes Linear Statistics: Theory and Methods

written by Michael Goldstein and David Wooff, published April 2007 by John Wiley & Sons Ltd., Chichester. ISBN 978-0-470-01562-9. 508pp. You can buy a copy directly from Wiley, or from Amazon UK or Amazon US, or any good bookshop of course.

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.

## Errata

• Page 211. Line 2. The explanation of variance is raised from 60%, not 63%.
• Page 227. The y-axis label to figure 6.7(c) should refer to G_2, not G_0.
• Page 229. The y-axis label to figure 6.8(c) should refer to G_2, not G_0.
• Page 239. Line 9. In the definition of the diagonal matrix Lambda star, replace each "n" by "m" on the right-hand-side of the equation.
• Page 247. Fig. 7.2. The legends for D-Melanogaster and D-Hydei should be switched. The D-Hydei counts are given by the filled circles.
• Page 248. Fig. 7.3. The legends for D-Melanogaster and D-Hydei should be switched. The D-Hydei counts are given by the filled circles.
• Page 249. Fig. 7.4. The legends for D-Melanogaster and D-Hydei should be switched. The D-Hydei counts are given by the filled circles.
• Page 250. Fig. 7.5. The legends for D-Melanogaster and D-Hydei should be switched. The D-Hydei counts are given by the filled circles.
• Page 250. last two lines, D.Melanogaster and D.Hydei should be switched.
• Page 252. Lines 7-8, D.Melanogaster and D.Hydei should be switched.
• Page 253. Fig. 7.6. The legends for D-Melanogaster and D-Hydei should be switched. The D-Hydei counts are given by the filled circles.
• Page 269. The line before (8.20): replace "resolved" by "remaining".
• Page 497. The reference to Craig et. al. (2001) gives the wrong title. The title of the paper should be Bayesian forecasting for complex systems using computer simulators .