Name: Svetlana Ivanovna Rudnykh
Institution: Universidad Nacional de Colombia y Universidad del Atlántico, Colombia
Co-authors: Víctor Ignacio López, Profesor Asociado, Escuela de Estadística, Universidad Nacional de Colombia, Colombia
We consider the problem of construction penalized Bayesian optimal designs for nonlinear regression models. This investigation combines the Bayesian approach to experimental design and the use of desirable functions to specify design restrictions. The Bayesian approach to experimental design enables to incorporate prior information of unknown parameters, whereas the use of desirability functions helps to obtain optimal designs that fulfill practical design preferences imposed by an investigator. The methodology proposed in this work is illustrated by the two-parameter exponential regression model. Then, we compare designs obtained for different prior distributions of unknown parameters by efficiency calculations and simulation study. Results show that the D-efficiencies of the penalized designs with respect to the nonpenalized designs do not differ significantly. The mean squared error (MSE) values of the nonlinear term depend on the variance and skewness of the parameter prior distribution. The MSE values increase as the magnitude of these parameters increases.