A Bayes Linear Bayes Method for Estimation of Correlated Event Rates. Issue 12 (28th March 2013)

• Record Type: Journal Article
• Authors: Quigley, John; Wilson, Kevin J.; Walls, Lesley; Bedford, Tim
• Is Part Of: Risk analysis. Volume 33:Issue 12(2013)
• Page Start: 2209
• Page End: 2224
• Publication Date: 2013-03-28
• Subjects: Technology -- Risk assessment -- Periodicals; 658.403
• DOI: 10.1111/risa.12035
• Languages: English
• ISSNs: 0272-4332

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>Typically, full Bayesian estimation of correlated event rates can be computationally challenging since estimators are intractable. When estimation of event rates represents one activity within a larger modeling process, there is an incentive to develop more efficient inference than provided by a full Bayesian model. We develop a new subjective inference method for correlated event rates based on a Bayes linear Bayes model under the assumption that events are generated from a homogeneous Poisson process. To reduce the elicitation burden we introduce homogenization factors to the model and, as an alternative to a subjective prior, an empirical method using the method of moments is developed. Inference under the new method is compared against estimates obtained under a full Bayesian model, which takes a multivariate gamma prior, where the predictive and posterior distributions are derived in terms of well‐known functions. The mathematical properties of both models are presented. A simulation study shows that the Bayes linear Bayes inference method and the full Bayesian model provide equally reliable estimates. An illustrative example, motivated by a problem of estimating correlated event rates across different users in a simple supply chain, shows how ignoring the correlation leads to biased estimation of event rates.</p> </abstract>