Bayesian Analysis of Multifidelity Computer Models With Local Features and Nonnested Experimental Designs: Application to the WRF Model

Motivated by a multi-fidelity Weather Research and Forecasting (WRF) climate model application where the available simulations are not generated based on hierarchically nested experimental design, we develop a new co-kriging procedure called augmented Bayesian treed co-kriging. The proposed procedure extends the scope of co-kriging in two major ways. We introduce a binary treed partition latent process in the multifidelity setting to account for nonstationary and potential discontinuities in the model outputs at different fidelity levels. Moreover, we introduce an efficient imputation mechanism which allows the practical implementation of co-kriging when the experimental design is nonhierarchically nested by enabling the specification of semiconjugate priors. Our imputation strategy allows the design of an efficient reversible jump Markov chain Monte Carlo implementation that involves collapsed blocks and direct simulation from conditional distributions. We develop the Monte Carlo recursive emulator which provides a Monte Carlo proxy for the full predictive distribution of the model output at each fidelity level, in a computationally feasible manner. The performance of our method is demonstrated on benchmark examples and used for the analysis of a large-scale climate modeling application which involves the WRF model.