Pseudo-Bayesian Optimal Designs for Fitting Fractional Polynomial Response Surface Models

TL;DR

This paper develops Bayesian optimal exact experimental designs for fractional polynomial response surface models, improving parameter estimation efficiency and comparing these designs to standard alternatives.

Contribution

It applies a recent methodology to find Bayesian optimal designs specifically for fractional polynomial models, enhancing experimental design strategies.

Findings

Bayesian optimal designs outperform standard designs in efficiency.

The methodology provides exact designs suitable for nonlinear models.

Comparison shows improved parameter estimation with proposed designs.

Abstract

Fractional polynomial models are potentially useful for response surfaces investigations. With the availability of routines for fitting nonlinear models in statistical packages they are increasingly being used. However, as in all experiments the design should be chosen such that the model parameters are estimated as efficiently as possible. The design choice for such models involves the known nonlinear models' design difficulties but \cite{gilmour_trinca_2012b} proposed a methodology capable of producing exact designs that makes use of the computing facilities available today. In this paper, we use this methodology to find Bayesian optimal exact designs for several fractional polynomial models. The optimum designs are compared to various standard designs in response surface problems.