Efficient Bayesian designs under heteroscedasticity

Abstract

In optimum design theory designs are constructed that maximize the information on the unknown parameters of the response function. The major part deals with designs optimal for response function estimation under the assumption of homoscedasticity. In this paper, optimal designs are derived in case of multiplicative heteroscedasticity for either response function estimation or response and variance function estimation by using a Bayesian approach. The efficiencies of the Bayesian designs derived with various priors are compared to those of the classic designs with respect to various variance functions. The results show that any prior knowledge about the sign of the variance function parameters leads to designs that are considerably more efficient than the classic ones based on homoscedastic assumptions.