Title: A Bayesian analysis of the extended Poisson regression
Authors: Haruhiko Shimizu - Kobe University (Japan) [presenting]
Abstract: The Bayesian analysis of the extended Poisson regression model is considered. The support of the extended Poisson distribution includes not only the non-negative integers but also negative integers. The usual Poisson distribution is a special case of the extended Poisson distribution. We study the Bayesian estimation of the parameters of extended Poisson distribution and show that Bayesian analysis performed better than maximum likelihood method. In particular, Bayesian method was better in estimating the parameter of the ratio of positive or negative values in the dataset when the ratio is close to zero or one. In these cases, maximum likelihood method was not available since the Hessian did not converge for some cases. As for Bayesian method, we are able to estimate the ratio parameter if we choose the appropriate prior density. Based on the previous study, we next construct the extended Poisson regression model. We then compare the Bayesian method and maximum likelihood method for estimating the parameters of the extended Poisson regression model. We also consider an application of this model.