Penalized Bayesian D-Optimal Designs for Regression Models of Continuous Response

Abstract

We propose extending the use of desirability functions in Bayesian optimal designs for regression models. This technique generates experimental designs with good statistical inference properties according to Bayesian optimal design theory and practical features, as defined by an investigator. These practical features are defined by a penalty function, using an overall desirability function, which is added to a Bayesian $D$-optimal design criterion to penalize impractical experimental designs. This methodology is illustrated by two examples of regression models: quadratic and exponential. Then, we compare designs obtained for different prior distributions of unknown parameters by efficiency calculations and simulation study. Results show that the $D$-efficiencies of the penalized designs relative to the non-penalized Bayesian D-optimal designs are competitive.