Bayesian Optimization for a Chemical Reaction Using a Nonlinear Mixed-Effects Model

• Activity Number: 552
• Type: Topic Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Richard Lewis*+ and Brian Crump and Zifang Guo and John J. Peterson
• Companies: GlaxoSmithKline and GlaxoSmithKline and North Carolina State University and GlaxoSmithKline
• Keywords: Nonlinear Model ; Mechanistic Model ; Bayesian Methods ; Mixed-Effects Model

Abstract

Non-linear mechanistic models are often used to model chemical reactions, with a goal of setting optimal reaction conditions (e.g. catalyst loading, reagent concentrations, reaction temperature, and reaction time). The model parameters are generally considered to be fixed effects, but this can lead to difficulty modeling run-to-run differences in experimental results. We add random intercept and slope effects to a mechanistic model in order to account for run-to-run differences, using Bayesian methodology (WinBUGS). Following Peterson (2004), the resulting posterior predictive distribution is used to determine the probability that a specified set of reaction conditions will produce acceptable results. We illustrate our approach using an example in which most of the variability in the reaction process is due to run-to-run variation. It is therefore critical to model this variation when assessing process reliability for meeting specifications.