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Bayes linear kinematics and Bayes linear Bayes graphical models

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  • Michael Goldstein

Abstract

Probability kinematics (Jeffrey, 1965, 1983) furnishes a method for revising a prior probability specification based upon new probabilities over a partition. We develop a corresponding Bayes linear kinematic for a Bayes linear analysis given information which changes our beliefs about a random vector in some generalised way. We derive necessary and sufficient conditions for commutativity of successive Bayes linear kinematics which depend upon the eigenstructure of the joint kinematic resolution transform. As an application we introduce the Bayes linear Bayes graphical model, which is a mixture of fully Bayesian and Bayes linear graphical models, combining the simplicity of Gaussian graphical models with the ability to allow conditioning on marginal distributions of any form, and exploit Bayes linear kinematics to embed full conditional updates within Bayes linear belief adjustments. The theory is illustrated with a treatment of partition testing for software reliability. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Michael Goldstein, 2004. "Bayes linear kinematics and Bayes linear Bayes graphical models," Biometrika, Biometrika Trust, vol. 91(2), pages 425-446, June.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:2:p:425-446
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    Cited by:

    1. F. P. A. Coolen & M Goldstein & D. A. Wooff, 2007. "Using Bayesian statistics to support testing of software systems," Journal of Risk and Reliability, , vol. 221(1), pages 85-93, March.
    2. K J Wilson & M Farrow, 2010. "Bayes linear kinematics in the analysis of failure rates and failure time distributions," Journal of Risk and Reliability, , vol. 224(4), pages 309-321, December.
    3. John Quigley & Kevin J. Wilson & Lesley Walls & Tim Bedford, 2013. "A Bayes Linear Bayes Method for Estimation of Correlated Event Rates," Risk Analysis, John Wiley & Sons, vol. 33(12), pages 2209-2224, December.
    4. Goldstein, Michael & Bedford, Tim, 2007. "The Bayes linear approach to inference and decision-making for a reliability programme," Reliability Engineering and System Safety, Elsevier, vol. 92(10), pages 1344-1352.

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