A novel class of mixed Poisson distributions and wastewater-based epidemiology

Mixed Poisson families are widely used to model count data with overdispersion, zero inflation, or heavy tails in a variety of applications including finance, biology, and the physical sciences. The mixing distribution assigned to the Poisson rate is typically restricted to have nonnegative support. Surprisingly, this assumption is unnecessary. For example, the Hermite distribution is analogous to mixing a Poisson with an untruncated Gaussian and can be derived using generating functions so long as constraints on the natural parameter are satisfied. I will give a general characterization of this unusual class as well as several concrete examples, including an apparently novel generalization of the discrete stable family. I will also briefly present some applied work in wastewater-based epidemiology examining spatiotemporal variation of the pepper mild mottle virus biomarker. 

To join this seminar virtually, please request Zoom connection details from hr.ops@stat.ubc.ca.