Bayes Linear Methods II
An example with an introduction to [B/D]

David Wooff
University of Durham

[B/D] Home Page: http://fourier.dur.ac.uk:8000/stats/bd/

Abstract:

This article is one of a series of papers and technical reports describing Bayes linear methods. Our purpose is to introduce both the approach and the computer implementation of the approach, the programming language [B/D], by way of a simple (but genuine) example. The three parts of this article contain (i) the establishment of the example, concerning the oral glucose tolerance test used in diagnosing diabetes; (ii) a Bayes linear analysis of the example to explore some of the main features of the approach; and (iii) a tutorial in the use of the subjectivist statistical programming language [B/D] used to perform the analysis for the example.

• Introduction and motivation
  • Organisation of this document
  • Why Bayes linear methods?
  • Establishing the example
    • Expectation specifications
    • Covariance specifications
    • Data specifications
    • Remarks about the example
• The Bayes linear approach by example
  • Adjusting beliefs by data
    • Adjusted expectations
    • Adjusted variances
    • Adjusting a collection of quantities
    • Canonical directions
    • Adjusting the canonical belief structure
  • Observing the adjustment
    • Standardised observations
    • Evaluating the adjusted expectation
    • Standardised adjusted expectations
    • Consistency checks for the canonical directions
    • The size and bearing of the adjustment
  • Adjusting beliefs in stages
    • Performing the initial adjustment
    • Partial adjustments of belief
      • Partial variances
      • Partial canonical directions
      • Partial expectations
      • The size of the partial adjustment
      • The bearing and path correlation for the partial adjustment
    • Withdrawing quantities from the adjustment
  • Review of the example
• An introduction to the [B/D] language
  • Introducing [B/D]
    • Starting [B/D]
    • [B/D] Command Lines
  • Organising inputs to [B/D]
    • Declaring quantities
    • Collections of quantites
    • Specifying beliefs
    • Inputting data
  • Adjusting beliefs by data
    • Performing an adjustment
    • Adjusted expectations
    • Adjusted variances
    • Canonical directions
  • Observing the adjustment
    • Evaluating the adjusted expectation
    • Consistency checks for the canonical directions
    • Viewing the size and direction of adjustment
  • Further [B/D] techniques
    • Generating the canonical directions
    • [B/D] Assignments
    • Building assignments
    • Using the constructed quantities
    • Constructing the bearing
  • Adjusting beliefs in stages
    • The initial adjustment
    • Subsequent partial adjustments
      • Partial variances
      • Partial canonical directions
      • Further results for the partial adjustment
    • Withdrawing quantities from the adjustment
  • Review of [B/D] usage
• References
• About this document ...