Abstract: It is, more often than not, difficult to gain the concret posterior distribution of Poisson regression after priori distribution of parameters is given. This paper provides an approximate likelihood function of the parameters according to the property of the large sample of Γdistribution and their approximate posterior distribution. The simulation study shows that the Bayesian estimation performs well based on the approximate posterior distribution.

Key words: quadratic loss funtion, Poisson regression, approximate Bayes estimation, parameter, prioridistribution, posterior distribution, likelihood function