Bayesian Treed Calibration: An Application to Carbon Capture With AX Sorbent

In cases where field (or experimental) measurements are not available, computer models can model real physical or engineering systems to reproduce their outcomes. They are usually calibrated in light of experimental data to create a better representation of the real system. Statistical methods, based on Gaussian processes, for calibration and prediction have been especially important when the computer models are expensive and experimental data limited. In this article, we develop the Bayesian treed calibration (BTC) as an extension of standard Gaussian process calibration methods to deal with nonstationarity computer models and/or their discrepancy from the field (or experimental) data. Our proposed method partitions both the calibration and observable input space, based on a binary tree partitioning, into subregions where existing model calibration methods can be applied to connect a computer model with the real system. The estimation of the parameters in the proposed model is carried out using Markov chain Monte Carlo (MCMC) computational techniques. Different strategies have been applied to improve mixing. We illustrate our method in two artificial examples and a real application that concerns the capture of carbon dioxide with AX amine based sorbents. The source code and the examples analyzed in this article are available as part of the supplementary materials.