B ayesian Count Models

Abstract

Abstract Bayesian count models are aligned with frequentist‐based count models; that is, they are based on the same underlying distributions as are standard count models estimated using maximum likelihood and quadrature. The key difference in Bayesian models, however, is that the parameters to be estimated are assumed to be randomly distributed, whereas the data are fixed. In addition, each parameter in the model is mixed with a “prior” distribution defining information related to the parameter but which is external to the data upon which the model likelihood is based. The product of the (log)likelihood and prior distributions define the posterior parameters in the model. Basic Bayesian count models include Poisson, negative binomial, generalized Poisson, zero‐inflated and hurdle models, related hierarchical models, and a variety of other mixture count models. Code is provided using R, JAGS, Python/Stan, INLA, and Stata for a Bayesian Poisson model on synthetic data. JAGS, SAS, and Stata code are provided for a Bayesian negative binomial model; JAGS and Stata code are displayed for a Bayesian zero‐inflated negative binomial model.