z-logo
Premium
A Bayes Linear Bayes Method for Estimation of Correlated Event Rates
Author(s) -
Quigley John,
Wilson Kevin J.,
Walls Lesley,
Bedford Tim
Publication year - 2013
Publication title -
risk analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.972
H-Index - 130
eISSN - 1539-6924
pISSN - 0272-4332
DOI - 10.1111/risa.12035
Subject(s) - bayes' theorem , bayesian inference , bayesian probability , inference , event (particle physics) , bayes factor , computer science , bayesian linear regression , estimator , econometrics , linear model , statistics , mathematics , artificial intelligence , machine learning , physics , quantum mechanics
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.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here