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A Bayes linear Bayes method for estimation of correlated event rates

Lookup NU author(s): Professor Kevin WilsonORCiD

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).

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.

Publication metadata

Author(s): Quigley J, Wilson KJ, Walls L, Bedford T

Publication type: Article

Publication status: Published

Journal: Risk Analysis

Year: 2013

Volume: 33

Issue: 12

Pages: 2209-2224

Print publication date: 01/12/2013

Online publication date: 28/03/2013

Acceptance date: 28/01/2013

Date deposited: 23/09/2015

ISSN (print): 0272-4332

ISSN (electronic): 1539-6924

Publisher: Wiley

URL: http://dx.doi.org/10.1111/risa.12035

DOI: 10.1111/risa.12035

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