Bayesian Methods for Process Optimization

The mainstream literature on Response Surface Optimization is classical or “frequentist” given that it considers parameters as unknown constants that need to be estimated from data. The sampling variability or experimental error is reflected in the sampling distributions of the estimates. This sampling variability can (and should) be considered in optimization, see Chapter 7. In contrast, the Bayesian approach to statistical inference considers model parameters (and in fact, any unknowns) as random variables. This has considerable advantages over the classical approach when optimizing a process based on a fitted model, since depending on the estimated parameters different optimal conditions will be determined. In the Bayesian approach, the uncertainty in the model’s parameters is directly incorporated in the analysis. Prior knowledge (which can be considerable, in agreement with Weiner’s quote above) can be incorporated, if desired, into the optimization process. Otherwise, non-informative priors can be used for optimization purposes.

This chapter presents Bayesian linear regression models and its use in process optimization, with the minimum number of technical details, without sacrificing understanding of the main ideas for readers not familiar with Bayesian Analysis.