Data analytic tools for understanding random field regression models

Random field regression (RFR) models, in which a response is treated as the realization of a random field, have been advocated for modeling data from experiments in high signal-to-noise settings. In particular, RFR models have proven useful in analyzing data generated from computer simulations of complex processes. They offer flexibility for smoothing these data and are able to interpolate the known values for factor settings tested on the simulator. However, these models lack the easy interpretability of standard regression estimators. Our purpose in this article is to demonstrate that there is actually much common ground between the RFR models and Bayesian regression and to provide some simple data-analytic tools that can help expose a regression model associated with an RFR model.