05446nam 2200673 a 450 991083043090332120230721030022.01-280-85495-297866108549500-470-06566-40-470-06567-2(CKB)1000000000357364(EBL)292573(OCoLC)476052538(SSID)ssj0000109289(PQKBManifestationID)11145290(PQKBTitleCode)TC0000109289(PQKBWorkID)10047352(PQKB)10686582(MiAaPQ)EBC292573(EXLCZ)99100000000035736420061010d2007 uy 0engur|n|---|||||txtccrBayes linear statistics[electronic resource] theory and methods /Michael Goldstein and David WooffChichester, England ;Hoboken, NJ John Wileyc20071 online resource (538 p.)Wiley series in probability and statisticsDescription based upon print version of record.0-470-01562-4 Includes bibliographical references (p. [497]-502) and index.Bayes Linear Statistics; Contents; Preface; 1 The Bayes linear approach; 1.1 Combining beliefs with data; 1.2 The Bayesian approach; 1.3 Features of the Bayes linear approach; 1.4 Example; 1.4.1 Expectation, variance, and standardization; 1.4.2 Prior inputs; 1.4.3 Adjusted expectations; 1.4.4 Adjusted versions; 1.4.5 Adjusted variances; 1.4.6 Checking data inputs; 1.4.7 Observed adjusted expectations; 1.4.8 Diagnostics for adjusted beliefs; 1.4.9 Further diagnostics for the adjusted versions; 1.4.10 Summary of basic adjustment; 1.4.11 Diagnostics for collections1.4.12 Exploring collections of beliefs via canonical structure1.4.13 Modifying the original specifications; 1.4.14 Repeating the analysis for the revised model; 1.4.15 Global analysis of collections of observations; 1.4.16 Partial adjustments; 1.4.17 Partial diagnostics; 1.4.18 Summary; 1.5 Overview; 2 Expectation; 2.1 Expectation as a primitive; 2.2 Discussion: expectation as a primitive; 2.3 Quantifying collections of uncertainties; 2.4 Specifying prior beliefs; 2.4.1 Example: oral glucose tolerance test; 2.5 Qualitative and quantitative prior specification2.6 Example: qualitative representation of uncertainty2.6.1 Identifying the quantities of interest; 2.6.2 Identifying relevant prior information; 2.6.3 Sources of variation; 2.6.4 Representing population variation; 2.6.5 The qualitative representation; 2.6.6 Graphical models; 2.7 Example: quantifying uncertainty; 2.7.1 Prior expectations; 2.7.2 Prior variances; 2.7.3 Prior covariances; 2.7.4 Summary of belief specifications; 2.8 Discussion: on the various methods for assigning expectations; 3 Adjusting beliefs; 3.1 Adjusted expectation; 3.2 Properties of adjusted expectation3.3 Adjusted variance3.4 Interpretations of belief adjustment; 3.5 Foundational issues concerning belief adjustment; 3.6 Example: one-dimensional problem; 3.7 Collections of adjusted beliefs; 3.8 Examples; 3.8.1 Algebraic example; 3.8.2 Oral glucose tolerance test; 3.8.3 Many oral glucose tolerance tests; 3.9 Canonical analysis for a belief adjustment; 3.9.1 Canonical directions for the adjustment; 3.9.2 The resolution transform; 3.9.3 Partitioning the resolution; 3.9.4 The reverse adjustment; 3.9.5 Minimal linear sufficiency; 3.9.6 The adjusted belief transform matrix3.10 The geometric interpretation of belief adjustment3.11 Examples; 3.11.1 Simple one-dimensional problem; 3.11.2 Algebraic example; 3.11.3 Oral glucose tolerance test; 3.12 Further reading; 4 The observed adjustment; 4.1 Discrepancy; 4.1.1 Discrepancy for a collection; 4.1.2 Evaluating discrepancy over a basis; 4.1.3 Discrepancy for quantities with variance zero; 4.2 Properties of discrepancy measures; 4.2.1 Evaluating the discrepancy vector over a basis; 4.3 Examples; 4.3.1 Simple one-dimensional problem; 4.3.2 Detecting degeneracy; 4.3.3 Oral glucose tolerance test4.4 The observed adjustmentBayesian 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, methodolWiley series in probability and statistics.Bayesian statistical decision theoryLinear systemsComputational complexityBayesian statistical decision theory.Linear systems.Computational complexity.519.5519.542Goldstein Michael1949-1647684Wooff David311186MiAaPQMiAaPQMiAaPQBOOK9910830430903321Bayes linear statistics3995407UNINA