On the Bayesian treed multivariate Gaussian process with linear model of coregionalization

The Bayesian treed multivariate Gaussian process (BTMGP) and Bayesian treed Gaussian process (BTGP) provide straightforward mechanisms for emulating non-stationary multivariate computer codes that alleviate computational demands by fitting models locally. Here, we show that the existing BTMGP performs acceptably when the output variables are dependent but unsatisfactory when they are independent while the BTGP performs contrariwise. We develop the BTMGP with linear model of coregionalization (LMC) cross-covariance, an extension of the BTMGP, that gives satisfactory fitting compared to the other two emulators regardless of whether the output variables are locally dependent. The proposed BTMGP is able to locally model more complex and realistic cross-covariance functions. The conditional representation of LMC in combination with the right choice of the prior distributions allow us to improve the MCMC mixing and invert smaller matrices in the Bayesian inference. We illustrate our empirical results and the performance of the proposed method through artificial examples, and one application to the multiphase flow in a full scale regenerator of a carbon capture unit.