  It has become commonplace to use complex computer models to predict outcomes
in regions where data does not exist. Typically these models need to be
calibrated and validated using some experimental data, which often consists of
multiple correlated outcomes. In addition, some of the model parameters may be
categorical in nature, such as a pointer variable to alternate models (or
submodels) for some of the physics of the system. Here we present a general
approach for calibration in such situations where an emulator of the
computationally demanding models and a discrepancy term from the model to
reality are represented within a Bayesian Smoothing Spline (BSS) ANOVA
framework. The BSS-ANOVA framework has several advantages over the traditional
Gaussian Process, including ease of handling categorical inputs and correlated
outputs, and improved computational efficiency. Finally this framework is then
applied to the problem that motivated its design; a calibration of a
computational fluid dynamics model of a bubbling fluidized which is used as an
absorber in a CO2 capture system.
