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Title: A Bayesian analysis of extended Poisson distribution Authors:  Haruhiko Shimizu - Kobe University (Japan) [presenting]
Abstract: A Bayesian analysis of extended Poisson distribution is considered, which can be applied to non-negative integers as well as the negative integers. The distribution has two parameters, lambda, which is related to the mean of the distribution, and $p$, which is the ratio of the positive integers. Maximum likelihood estimators of these parameters are analytically solved and shown that they are asymptotically independent. We can check the independence of the parameters by computing the correlation matrix of the parameters. However, if we try to compute the maximum likelihood estimators of these two parameters jointly, we often find that likelihood function as well as the parameters does not converge. We try to apply the Bayesian analysis and compute the parameters using Markov chain Monte Carlo, and compare with the maximum likelihood estimation. Based on the distribution histogram of the extended Poisson distribution, we use bimodal distribution as a proposal density. Poisson regression model can explain the non-negative integers. Using the extended Poisson distribution, we are able to use all the integers as explained variable of the regression model. As an extension, we consider the extended Poisson regression model.