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 semi parametric 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.