Bayesian D-Optimal Design for Poisson Regression Model with Random Effect

The main researches of optimum experimental designs for mixed effects have been concentrated on locally optimal designs. These designs are obtained based on the initial guess of parameters. Therefore، locally designs may be the best design but for wrong assumed model. Recently، Bayesian approach has been considered by researches when information about model parameters is available. In the present work، optimal design for the mixed effects Poisson regression model based on some prior distributions are considered and for two special cases of this models the Bayesian D-optimal designs are obtained for some representative values of variance of random effect. The results are compared to Poisson regression model without random effects.