LEADER 05398nam 2200661 a 450 001 9910876938403321 005 20200520144314.0 010 $a1-280-85495-2 010 $a9786610854950 010 $a0-470-06566-4 010 $a0-470-06567-2 035 $a(CKB)1000000000357364 035 $a(EBL)292573 035 $a(OCoLC)476052538 035 $a(SSID)ssj0000109289 035 $a(PQKBManifestationID)11145290 035 $a(PQKBTitleCode)TC0000109289 035 $a(PQKBWorkID)10047352 035 $a(PQKB)10686582 035 $a(MiAaPQ)EBC292573 035 $a(EXLCZ)991000000000357364 100 $a20061010d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aBayes linear statistics $etheory and methods /$fMichael Goldstein and David Wooff 210 $aChichester, England ;$aHoboken, NJ $cJohn Wiley$dc2007 215 $a1 online resource (538 p.) 225 1 $aWiley series in probability and statistics 300 $aDescription based upon print version of record. 311 $a0-470-01562-4 320 $aIncludes bibliographical references (p. [497]-502) and index. 327 $aBayes 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 collections 327 $a1.4.12 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 specification 327 $a2.6 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 expectation 327 $a3.3 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 matrix 327 $a3.10 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 test 327 $a4.4 The observed adjustment 330 $aBayesian methods combine information available from data with any prior information available from expert knowledge. The Bayes linear approach follows this path, offering a quantitative structure for expressing beliefs, and systematic methods for adjusting these beliefs, given observational data. The methodology differs from the full Bayesian methodology in that it establishes simpler approaches to belief specification and analysis based around expectation judgements. Bayes Linear Statistics presents an authoritative account of this approach, explaining the foundations, theory, methodol 410 0$aWiley series in probability and statistics. 606 $aBayesian statistical decision theory 606 $aLinear systems 606 $aComputational complexity 615 0$aBayesian statistical decision theory. 615 0$aLinear systems. 615 0$aComputational complexity. 676 $a519.5/42 700 $aGoldstein$b Michael$f1949-$01761762 701 $aWooff$b David$0311186 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910876938403321 996 $aBayes linear statistics$94201376 997 $aUNINA