Bayesian inference for pseudo-Poisson data

The bivariate pseudo-Poisson model discussed in this paper is one in which one marginal density and the conditional density of the other variable are both of the Poisson form. Such models find application for modelling bivariate count data with usually positive correlation. In the present note, we examine Bayesian estimation of the unknown parameters of bivariate pseudo-Poisson models utilizing independent gamma priors for the parameters as well as pseudo-gamma priors. Possible conjugacy is investigated in both full and submodels. In some special subcases, conjugate priors can be identified. A simulation study is included to illustrate the performance of Bayesian parameter estimates using a variety of priors, both informative and non-informative. The techniques are illustrated by re-analysing two well-known bivariate count data sets.