Imprecise Truncated Poisson Regression for Predictive Inference

• Activity Number: 698
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Chel Hee Lee*+ and Mikelis Bickis
• Companies: University of Saskatchewan and University of Saskatchewan
• Keywords: prior ignorance ; imprecise probability ; zero-truncated Poisson regression

Abstract

Prevalence is a valuable epidemiological measure about the burden of disease in a community for planning health services; however, the true prevalence is typically underestimated. Since there is no way to know the truth in practice, we aim to construct a framework for quantifying our epistemic ignorance about the estimate by applying the Walley's inferential paradigm. We restricted ourselves to zero-truncated Poisson sampling models that give an one-parameter exponential family with the canonical log-link function since zero counts are not observed. Normal and log-gamma priors are mainly studied on the canonical hyperparameter space by constructing a three-parameter exponential family of distributions which includes both priors. A canonical parametrization allows us to incorporate information about covariates into the model by equating them to a linear combination of regression parameters; thus, normal priors on regression parameters induce normal priors on canonical parameter in the form of a multiple parameter exponential family. Finally, we visualize a translation of this family of posteriors on the hyperparameter space and a decrease of prior ignorance by learning from data.