A Bayes linear Bayes method for estimation of correlated event rates

Quigley, John and Wilson, Kevin and Walls, Lesley and Bedford, Tim (2013) A Bayes linear Bayes method for estimation of correlated event rates. Risk Analysis, 33 (12). 2209–2224. ISSN 0272-4332

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    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.

    Creators(s): Quigley, John, Wilson, Kevin, Walls, Lesley ORCID logoORCID: https://orcid.org/0000-0001-7016-9141 and Bedford, Tim ORCID logoORCID: https://orcid.org/0000-0002-3545-2088;
    Item type:Article
    ID code:43403
    Keywords:reliability, correlated event rates, poisson process, bayes linear kinematics, empirical bayes, supply chain, Management. Industrial Management, Management Science and Operations Research
    Subjects:Social Sciences > Industries. Land use. Labor > Management. Industrial Management
    Department:Strathclyde Business School > Management Science
    Depositing user: Pure Administrator
    Date deposited:03 Apr 2013 13:55
    Last modified:24 Jan 2021 02:51
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/43403
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