Bayesian inference for bivariate Poisson data with zero-inflation.
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Drevets, Madeline L., 1991-
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Multivariate count data with zero-inflation is common throughout pure and applied science. Such count data often includes excess zeros. Zero-inflated Poisson regression models have been used in several applications to model bivariate count data with excess zeros. In this dissertation, we explore a Bayesian approach to bivariate Poisson models where either one or both counts is zero-inflated, with a primary focus on informative prior structures for these models. Bayesian treatments of zero-inflated Poisson models have focused on diffuse prior structures for model parameters. Nevertheless, we demonstrate that such an approach can be problematic with respect to convergence. We offer an informative prior approach, and propose methods of prior elicitation from a subject-matter expert. This includes exploration of methods for informative prior construction for an association parameter, and a multivariate distribution. We demonstrate our proposed methods within the context of a clinical example.