Bayesian Inference of Poisson Distribution using Conjugate and Non-Informative Priors

Poisson distribution is one of the most important and widely used statistical distributions. It is commonly used to describe thefrequency probability of specific events when the average probability of a single occurrence within a given time interval isknown. In this paper, Bayesian inference of Poisson distribution parameter (μ) is presented. Two Bayesian estimators of μusing two different priors are derived, one by using conjugate prior by applying gamma distribution, and the other usingnon-informative prior by applying Jeffery prior. The two priors yield the same posterior distributions namely gammadistribution. Comparison of the two Bayesian estimators is conducted through their bias and mean square error evaluation.