Bayesian optimal designs for probit regression with errors-in-variables

Abstract

Optimal design is the study of the choice of design points in an experiment. However, measurements are seldom precise in practical situations. If measurement error is substantial, it may ruin the whole experiment in that the objective of the experiment is not achieved. There is substantial literature on optimal designs, all based on the assumption that there is no measurement error in the covariates. For the Berkson error model, the observed design points are fixed by the experimenter but they deviate randomly from the pre-assigned level. In this paper, the Berkson error structure is incorporated into the probit regression model for which Bayesian D-optimal and A-optimal designs are studied. In addition, a new optimal design criterion is proposed.