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

Vicente G. Cancho, Bao Yiqi, Jose A. Fiorucci, Gladys D. C. Barriga, Dipak K. Dey

Communications in Statistics-Theory and Methods 47 (2018) 2741-2759

https://doi.org/10.1080/03610926.2017.1342839

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 ψ-divergence and several others, divergence measures, such as the Itakura–Saito, Kullback–Leibler, and χ2 divergence measures. Performance of our approach is illustrated in artificial, real apple cultivation experiment data, related to apple cultivation.