title: A Bayes linear Bayes method for estimation of correlated event rates.
abstract: 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.
authors.forename: John
authors.initials: J
authors.lastname: Quigley
authors.forename: Kevin J
authors.initials: KJ
authors.lastname: Wilson
authors.forename: Lesley
authors.initials: L
authors.lastname: Walls
authors.forename: Tim
authors.initials: T
authors.lastname: Bedford
keywords: Bayes linear kinematics; correlated event rates; empirical Bayes; homogenization factors; supply chain risk