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.
Quigley John, Wilson Kevin, Walls Lesley, Bedford 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 Tim, Walls 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 Matthew, Bedford 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 John, Bedford Tim, Walls 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)