Bayesian Generalized Linear Model for Difference of Over or Under Dispersed Counts

Oregon Convention Center 

Modelling the difference of two counts has many practical uses in statistics. The Skellam distribution can be used for such a model, however since the Skellam distribution is constructed as the difference of two Poisson distributions it is potentially unsuitable for modelling data that suffers from under or over dispersion. We take a first look at constructing a Bayesian generalized linear model for the difference of counts that can handle both under and over dispersion based on the difference of two Conway-Maxwell Poisson distribution (that is, a Conway-Maxwell Skellam distribution). The focus of this paper is on providing an explicit demonstration using the Metropolis-Hastings algorithm.

Count Data

Overdispersion

Underdispersion

Conway-Maxwell Skellam

Bayesian

Metropolis-Hastings 

IMS