Bayes Linear Methods I
Adjusting Beliefs: Concepts and Properties

Michael Goldstein
University of Durham

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

Abstract:

Bayes linear methodology provides a quantitative structure for expressing our beliefs and systematic methods for revising these beliefs given observational data. Particular emphasis is placed upon interpretation of and diagnostics for the specification. The approach is similar in spirit to the standard Bayes analysis, but is constructed so as to avoid much of the burden of specification and computation of the full Bayes case. This report is the first of a series describing Bayes linear methods. In this document, we introduce some of the basic machinery of the theory. Examples, computational issues, detailed derivations of results and approaches to belief elicitation will be addressed in related reports.

• Introduction
• Quantifying uncertainty
  • Quantifying uncertainty
  • Expectation
  • Belief specification
  • Belief structures
• Adjusting beliefs by data
  • Adjusted expectation
  • Interpretation
  • Adjusted variance
  • Adjusting a collection of quantities
  • Adjusted belief structures
  • Canonical directions
  • The system resolution uncertainty
• The observed adjustment
  • Standardised observations
  • Standardised adjustments
  • Canonical standardised adjustments
  • The bearing of the adjustment
  • The expected size of an adjustment
  • Data size
• Adjusting beliefs in stages
  • Partial adjustment of beliefs
  • Partial variance
  • Partial canonical directions
  • Representing the observed partial adjustment
  • Path correlation
  • Adjustment in several stages
• The geometry of belief adjustment
  • Belief adjustment
  • A comment on the choice of inner product
  • Belief transforms
  • Comparing inner products
  • The bearing
• References
• About this document ...