Maximum Information and Minimum Mean Posterior Variance Criteria for Response Surface Methodology

• Activity Number: 23
• Type: Contributed
• Date/Time: Sunday, August 3, 2003 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Shilpy Malla*+ and Michael R. Frey and Karl Gerlach
• Companies: Bucknell University and Bucknell University and Naval Research Laboratory

Abstract

Response surface methodology (RSM) is a suite of methods for determining features of an unknown system response. The response mode---the combination of the system control variable settings yielding the peak system response---is often of key interest. The mode and other response features are estimated in the RSM setting based on measurements of the system response. We consider estimating the response mode based on an interrogation, or sequence of measurements, of the response, adopting a Bayesian perspective to guide our interrogation. We propose two criteria, maximum information and minimum mean posterior variance, for optimally interrogating the system. We show in a simple example how each of these criteria along with current (a priori) knowledge of the mode from previous measurements determines the settings for the next measurement in the interrogation. Our example is a system with a single control variable and a unimodal response with additive exponential measurement error. Applying each of the two criteria, we obtain distinct, but qualitatively similar, rules for choosing the control variable setting in terms of simple conditions on the prior odds.