The Bayesian Analysis Of Zero-inflated Poisson Mixed Model Based On Dirichlet Process

Recently,zero-inflated Possion model with random effects has caused much at-tention of researchers.They usually assume the random effects follow normal distri-bution for convenience,which may be contrary with the reality in some cases.There-fore,the distribution of random effects is set to follow the Dirichlet process rather than a specific distribution to avoid a certain assumption for random effects in this paper.Then Bayes estimation of the model and related diagnosis are discussed.Fist of all,zero-inflated Poisson model with random effects based on Dirichelt process is considered in detail in the paper.The prior for random effects is a stick-breaking prior.A blocked Gibbs sampler and a Monte Carlo Markov Chain have been established to estimate parameters.Then,two goodness-fit statistics are computed to state the plausibility of the model;Bayes factor,pseudo-Bayes factor and deviance information criterion are given to compare the different models;K-L distance and Cook posterior mean distance are considered to find out the case influence points in the data.Meanwhile,in order to describe the effect of the time factor on the count data,an unknown smooth function is induced to semiparameter zero-inflated Poisson model based on the model above,and cubic B-splines are used to fit the unknown smooth function in the model.Similarly we also compute the Bayes estimation,goodness-fit statistics and influence points diagnosis for the model.Finally,the validity of Bayes estimation method and related statistics under different assumptions of random effects and different prior for parameters are studied based on stochastic simulation in detail.Besides of numerical simulation,the two models are also applied to a pharmaceutical data to get the estimation of the parameters,the distribution of random effects and the fitted curve of the unknown smooth function in the semiparameter model.