Bayes linear methods

Evaluation of uncertainty when information available includes both expert judgement and observed data is achieved typically using subjective Bayesian inference. This requires experts to describe their uncertainty through subjective probability distributions, referred to as the prior distribution, as it is prior to observing the data. However, defining such prior distributions over many unknowns which truly represents the judgements of an expert is a challenging task.

For complex models such as those found in risk and reliability analysis inference using Bayesian techniques can become prohibitively expensive computationally. Bayes linear methods are based on simple summaries such an means, correlations and standard deviations rather than requiring a fully specified probability distribution. The burden on experts in specifying prior information is much reduced and inference can be performed quickly and efficiently.

Our publications

Quigley John, Wilson Kevin, Walls LesleyBedford Tim, A Bayes linear Bayes method for estimation of correlated event rates Risk Analysis Vol 33, No. 12, pp. 2209–2224 (2013) 

Revie Matthew, Bedford TimWalls Lesley, Supporting reliability decisions during defence procurement using a Bayes linear methodology IEEE Transactions on Engineering Management Vol 58, No. 4, pp. 662-673 (2011) 

Revie MatthewBedford T.J., Walls L.A., Evaluation of elicitation methods to quantify Bayes linear models Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability Vol 224, No. 4, pp. 322-332 (2010)

Wilson Kevin, Farrow Malcolm, Bayes linear kinematics in the analysis of failure rates and failure time distributions Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability Vol 224, No. 4, pp. 309-321 (2010) 

Wilson Kevin, Quigley JohnBedford TimWalls Lesley, Bayes linear Bayes graphical models in the design of optimal test strategies International Journal of Performability Engineering Vol 9, No. 6, pp. 715-728 (2013)

Wisse B.W., Bedford T.J.Quigley J.L., Expert judgement combination using moment methods Reliability Engineering and System Safety Vol 93, No. 5, pp. 675-686 (2008)