Bayes Linear Statistics: Theory and MethodsBayesian 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:
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 | |
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 |
497 | |
503 | |
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Common terms and phrases
adjusted belief adjusted expectation adjusted variance analysis assess Bayes linear graphical beer belief adjustment belief specifications belief transform calculate canonical directions canonical quantities canonical resolutions canonical structure changes in expectation coefficients collection comparison conditional independence consistent construct corresponding covariance deﬁnite diagnostic diagram discrepancy vector eigenvalues eigenvectors elderly elements example Figure follows given glucose tolerance test Goldstein indicator functions inner product space inverse judgements junction tree Lemma linear combination linear graphical model mean component moral graph non-negative definite null space Observation number observed value parent node partial adjustment path correlation plot predictive prior expectation prior specification prior variance problem Property random quantities ratio regression representation residual variance resolved variance sample second-order exchangeable sequence sequential adjustments shading standard deviations standardized change statistical summary Suppose Table TB:D Theorem uncertainty uncorrelated Var(B variance matrix variance resolutions variance specifications variation week Zd(B zero