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An introduction to Bayes linear methods

Revie, Matthew and Bedford, Tim and Walls, Lesley (2007) An introduction to Bayes linear methods. In: Mathematical Methods in Reliability, 2007-05-08 - 2007-05-10.

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Abstract

Bayesian methods are common in reliability and risk assessment, however, such methods can demand a large amount of specification, can be computationally intensive and hence impractical for practitioners to use. The Bayes linear methodology is similar in spirit to a Bayesian approach but offers an alternative method of carrying out inference. Bayes linear methods are based on the use of expected values rather than probabilities, and updating is carried out by linear adjustment rather than by Bayes Theorem. The foundations of the method are very strong, based as they are in work of De Finetti and developed further by Goldstein. A Bayes linear model typically requires less specification than a corresponding probability model, and therefore, for a given amount of model building effort one can model a more complex situation. This paper aims to give the reader a brief insight into the Bayes linear methodology. This will be done by briefly discussing the philosophy of the approach, the theory of the approach, highlighting some benefits and limitations of the approach and ending with a brief example displaying the capabilities of the approach.