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An initial experimental design criteria is proposed for optimization problems by combining multiple, potentially competing, sources of prior information-engineering models, expert opinion, and data from past experimentation on similar, nonidentical systems. By leveraging prior information, resources used for the initial experiments are already targeted toward the optimization problem, potentially reducing the total number of resources needed in follow-up experimentation. New methodology, applicable to both computer and physical experiments, is provided for incorporating and combining conjectured models and data into both the initial modeling and experimental design stages. As a result, the experimental design criteria is flexible in how it balances space filling and objective oriented properties in the presence of conjectured prior information. An application to a thin-film growth study is provided in addition to a detailed numerical study of the design properties.
Key Words: Combined Information; Engineering Models; Expert Knowledge; Hierarchical Bayesian Model; Trust Model.
1. Introduction
When studying new and advanced technologies, there is often a lack of understanding of the true behavior of the process. In such cases, experimental designs are typically developed for exploratory purposes-spreading out points, in some sense uniformly, in attempt to understand and model the process as a whole. Because experimentation on new, advanced systems can be very costly, experimental designs that place points in regions that have little or no potential for being an optimal experimental input can be unnecessarily wasteful. Although a process may be new, prior sources of information can be present: researchers can conjecture expertopinion data based on decades of knowledge; engineering models may exist; and data from past experiments on similar, yet nonidentical, systems can provide insight into the new system.
By leveraging prior information, we propose a novel design criteria to use for solving optimization problems-problems with a goal of maximizing an objective function. The proposed methodology is applicable for both computer and physical experiments when the initial sample size is fixed before experimentation. Additionally, it can be used as a stand-alone design process or in conjunction with sequential experimental design procedures such as the SMED procedure of Dasgupta (2007), expected improvement designs (see Santner et al. (2003)), or any other designs for optimization.
The success of our approach stems from the ability to build an accurate prior model to estimate...