Bayesian optimal design for non-linear model under non-regularity condition

Abstract

The common classical approach for finding optimal design is minimizing the variance of an unbiased maximum likelihood estimator (MLE) of parameters. However, under regularity condition, the variance of MLE is approximated by the Cramer–Rao lower bound. In this article, optimal designs are obtained under non-regularity condition in non-linear models. In the Bayesian approach, conditional mutual information is used to propose a new optimality criterion; Bayesian optimal design maximizes the mutual information between the observation and the model parameters. A Bayesian compound criterion is also provided to facilitate the performance comparison of the optimal designs. Finally, the equivalence theorem is given for criterion to allow for checking the optimality of the obtained Bayesian design points.