Bayes Linear Statistics
Theory and Methods
Michael Goldstein and David Wooff
Durham University, UK
Preface xvii
1 The Bayes linear approach 1
1.1 Combiningbeliefswithdata .................... 2
1.2 TheBayesianapproach ....................... 3
1.3 Features of the Bayes linear approach . . . . . . . . . . . . . . . 6
1.4 Example ............................... 7
1.5 Overview............................... 30
2 Expectation 33
2.1 Expectation as a primitive . . . . . . . . . . . . . . . . . . . . . . 33
2.2 Discussion: expectation as a primitive . . . . . . . . . . . . . . . 35
2.3 Quantifying collections of uncertainties . . . . . . . . . . . . . . 37
2.4 Specifyingpriorbeliefs ....................... 39
2.5 Qualitative and quantitative prior specification . . . . . . . . . . . 41
2.6 Example: qualitative representation of uncertainty . . . . . . . . . 42
2.7 Example:quantifyinguncertainty.................. 48
2.8 Discussion: on the various methods for assigning expectations . . 52
3 Adjusting beliefs 55
3.1 Adjustedexpectation ........................ 55
3.2 Propertiesofadjustedexpectation ................. 56
3.3 Adjustedvariance .......................... 57
3.4 Interpretations of belief adjustment . . . . . . . . . . . . . . . . . 58
3.5 Foundational issues concerning belief adjustment . . . . . . . . . 60
3.6 Example:one-dimensionalproblem ................ 63
3.7 Collectionsofadjustedbeliefs ................... 64
3.8 Examples............................... 65
3.9 Canonical analysis for a belief adjustment . . . . . . . . . . . . . 75