Dπ-optimal designs for heteroscedastic nonlinear models: A robustness study (2020)
Optimal designs are used to determine the best conditions where an experiment should be performed to obtain certain statistical properties. In heteroscedastic nonlinear models where variance is a function of the mean, the optimality criterion depends on the choice of a local value for the model parameters. One way to avoid this dependency is to consider an a priori distribution for the vector of model parameters and incorporate it into the optimality criterion to be optimized. This paper considers D-optimal designs in heteroscedastic nonlinear models when a prior distribution associated with the model parameters is incorporated. The equivalence theorem is extended by considering the effect of the prior distribution. A methodology for the construction of discrete and continuous prior distributions is proposed. It is shown, with an example, how optimal designs can be found from the constructed distributions with a greater number of experimental points than those obtained with a local value. The efficiency of the designs found is very competitive compared to the optimal local designs. Additionally, prior distributions of a scale family are considered, and it is shown that the designs found are robust to the choice of the prior distribution chosen from this family.