Bayes Linear Methods III - Analysing Bayes linear influence diagrams and Exchangeability in [B/D]

David Wooff and 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 adjusting these beliefs given observational data. In this report we introduce two aspects of the methodology. Firstly, we discuss Bayes linear influence diagrams, which are tools for representing and interpreting both the qualititative and quantitative structure. Secondly, we address the basic role of exchangeability. The computer language [B/D] (an acronym for beliefs adjusted by data) has been developed to implement Bayes linear methods, and can be used to construct such influence diagrams. In this technical report, we show how [B/D] is used to generate various types of influence diagram for a simple, but non-trivial, problem. We also present an example which shows how [B/D] is used to exploit exchangeability. The example concerns a collection of exchangeable dynamic linear models, representing the reduction of alumina by electrolysis.

• Introduction
• Bayes linear influence diagrams
  • Example problem
  • The model
  • Prior beliefs
  • Establishing and generating the model
  • Assessing information content and flow for each yield separately
  • Influence diagrams summarising sequential knowledge acquisition
• Exploring sensitivity for exchangeable regressions
  • Exchangeability
  • Problem summary
  • Modelling and analysis
  • Other remarks
• Acknowledgements
• References
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