Graphical techniques for the assessment of Bayesian optimal designs

Abstract

Response surface methodology is a well-developed paradigm of statistical design and analysis that involves design of experiments, collection of data, conduction of regression analysis and evaluation of the fitted relationship between the factors and the response. Prediction capability is considered a vital aspect in response surface methodology as it reveals essential aspects of a process or system. Comparisons of designs' prediction efficiency based on single-valued efficiency-type criteria may not be always desirable. Thus, graphical techniques like variance dispersion graphs and fraction of design space plots were introduced which focus on the evaluation of the prediction performance of the designs. These graphical tools display the prediction capability of the designs over the entire design region.

Popular optimal designs, such as D-optimal designs, are constructed based on an assumed model. To reduce the model dependency, Bayesian designs were proposed. However, the variance dispersion graphs and the fraction of design space plots in the literature are not applicable to Bayesian designs. In this thesis, we developed the graphs for Bayesian designs. We created the graphs for 24-run 3-level Bayesian optimal designs with 3 factors and 30-run 3-level Bayesian optimal designs with 4 factors. Comparisons are made among the Bayesian optimal designs.