Locally, Bayesian and non parametric Bayesian optimal designs for unit exponential regression model

Abstract

. This study introduces optimal designs for the unit exponential (UE) non linear model using local, Bayesian, and non parametric Bayesian approaches. In the local approach, optimal designs were derived by substituting initial estimates for the unknown parameters. However, recognizing the inefficiency of these designs when initial estimates are distant from their true values, we adopted a Bayesian approach, employing the D-optimal criterion with uniform and truncated normal prior distributions for unknown parameters. In situations lacking informative or historical knowledge of parameters, a non parametric Bayesian approach was employed, incorporating the Dirichlet Process (DP) prior to the space of distribution functions. Finally, the efficiency of various optimal designs was analyzed for comparison.