Objective Bayes analysis of zero-inflated Poisson distribution with application to healthcare data

Abstract

In this article, non-informative priors are investigated for a zero-inflated Poisson distribution with two parameters: the probability of zeros and the mean of the Poisson part. Both the reference prior and the Jeffreys prior are derived and shown to be second-order matching priors when only the mean of the Poisson part is of interest. However, when the probability of zeros is of interest, the reference prior is still a second-order matching prior, whereas the Jeffreys prior is not so. Furthermore, when both parameters are of interest, the reference prior is a unique second-order matching prior. Frequentist coverage probabilities of the posterior confidence sets based on the Jeffreys and reference priors are compared with each other using Monte Carlo simulations and with confidence sets based on the maximum likelihood estimation.