A semiparametric Bayesian to Poisson mixed-effects model for Epileptics data

In the development of Poisson mixed-effects model(PMM), it is assumed that the distribution of random effects is normal. The normality assumption is likely to be violated in many practical researches. In this paper, we develop a semiparametric Bayesian approach for PMM by using a truncated and centered Dirichlet process(TCDP) prior to specify the distribution of random effects. A hybrid algorithm combining the Gibbs sampler and the Metropolis-Hastings algorithm is presented for obtaining the joint Bayesian estimates of unknown parameters and random effects and their standard errors. A simulation study and a real example are used to illustrate the proposed Bayesian methodologies.