Effect of a priori distributions in Bayesian D-optimal designs for a correlated non-linear model (2019)
In practice, complications can arise when constructing optimal designs for non-linear regression models. One of the major problems is when the observations are correlated, since they are taken from the same individual, object or experimental unit. When using the D-optimality criterion, it depends both on the parameter vector of the model and on the correlation structure assumed for the error term. One way to avoid this dependence is through the inclusion of a priori distributions in the D-optimality criterion. In this paper we study the effect of the choice of different a priori distributions, such as the Uniform, Gamma and Lognormal distributions in obtaining the D-optimal designs for a non-linear model, when the errors present different correlation structures. The designs are found by maximizing the approximate D-optimality criterion by the Monte Carlo method. In addition, a general methodology is proposed to find D-optimal designs for any type of non-linear model in the presence of correlated observations. Finally, it is proposed to compare the designs found by calculating the efficiencies taking as a reference design the one obtained with the a priori Uniform distribution. The methodology established in a case study is applied, and it is concluded that the designs obtained depend as much on the correlation structure as on the a priori distribution considered.