Estimation and influence diagnostics for zero-inflated hyper-Poisson regression model: full Bayesian analysis

Abstract

The purpose of this paper is to develop a Bayesian analysis for the zero-inflated hyper-Poisson model. Markov chain Monte Carlo methods are used to develop a Bayesian procedure for the model and the Bayes estimators are compared by simulation with the maximum-likelihood estimators. Regression modeling and model selection are also discussed and case deletion influence diagnostics are developed for the joint posterior distribution based on the functional Bregman divergence, which includes -divergence and several others, divergence measures, such as the Itakura-Saito, Kullback-Leibler, and (2) divergence measures. Performance of our approach is illustrated in artificial, real apple cultivation experiment data, related to apple cultivation.