Dπ-optimal designs for heteroscedastic nonlinear models: A robustness study

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Catalina Patiño-Bustamante https://orcid.org/0000-0001-6475-3624
Víctor López-Ríos https://orcid.org/0000-0003-2127-0221

Keywords

Optimal designs, information matrix, equivalence theorem, prior distribution, heteroscedastic models

Abstract

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.

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