D-optimal designs for linear mixed model with random effects of Dirichlet process

Abstract

This paper considers D-optimal designs for linear mixed models involving random effects with unknown distributions. From Bayesian point of view, the Dirichlet process as a prior distribution on the space of all distributions is used. Based on the Dirichlet process as a prior, we give the Bayes estimate of the density function of the response variable, which result in a mixture of two normal distributions. An explicit form of the Fisher information matrix for the proposed model is derived by using the Fourier transform and then D-optimal design is obtained by numerical calculations.

Keywords:

• D-optimal designs
• Dirichlet process
• Fourier transform
• Information matrix
• Linear mixed model