Bayesian Estimation of Parameters Correlation of Bivariate Poisson Distribution

In this study, based on Bayesian Generalized Linear Models, correlation between the parameters of two Poisson distributions was computed. Due to lack of the closed form for posterior distribution, hierarchical Bayesian statistics using the Metropolis-Hastings algorithm to calculate the correlation of two Poisson distributions is presented. In this regard, the highest posterior density for coefficient of variation in the model are calculated. Using Bayesian Deviance Information Criterion (DIC) has been shown that a Poisson-lognormal model can assess the correlation between the parameters better than the Poisson-gamma model. Finally, the proposed method is used to simulated data of BANK TEJARAT .