Integrated Analysis of Computational and Physical Experimental Data

Abstract

In scientific investigations, we frequently have data from computer experiment(s) as well as related physical experimental data on the same factors and related response variable(s). There may also exist one or more expert opinions regarding the response of interest. Traditional statistical approaches consider each of these sets of data separately with corresponding separate analyses and fitted statistical models. A compelling argument can be made that better, more precise statistical models can be obtained if we simultaneously analyze the combined data using a hierarchical Bayesian integrated modeling approach. However, such an integrated approach must recognize important differences, such as possible biases, in these experiments and expert opinions. We illustrate the methodology by using it to model the thermodynamic operation point of a top-spray fluidized bed microencapsulation processing unit. Such units are used in the food industry to tune the effect of functional ingredients and additives. An important thermodynamic response variable of interest, Y, is the steady-state outlet air temperature. In addition to a set of physical experimental observations involving six factors used to predict Y, similar results from three different computer models were also available. The integrated data from the physical experiment and the three computer models are used to fit an appropriate response surface (regression) model for predicting Y.