Bayesian improved model migration methodology for fast process modeling by incorporating prior information

We consider a Bayesian inference approach to enhance model migration, building on concepts laid out in an earlier paper (Lu and Gao, 2008a). Previous studies have been limited to a least-squares solution and have failed to take prior knowledge into consideration, possibly tending to cause overfitting and inaccurate estimations. We present a framework for Bayesian migration that can naturally incorporate and use prior information. The approach involves imposing normal-inverse-gamma priors over the migration parameter and exploring the resulting posterior distributions using a Markov chain Monte Carlo method. In addition, we provide a batch sequential design framework for iterative implementation of model migration, which thus avoids an exhaustive treatment of a predetermined number of design points. The effectiveness of these proposed methods is demonstrated using two examples: a numerical study and an injection molding process.