2013/03/28 by John Quigley, Kevin J. Wilson, Lesley Walls +1 · 2 citations
Decision Sciences · Computer Science · Mathematics · #Advanced Statistical Process Monitoring #Bayesian Methods and Mixture Models #Optimal Experimental Design Methods #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
paper · doi:10.1111/risa.12035
openalex publication_date 2013/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
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.