  We propose a multi-fidelity Bayesian emulator for the analysis of the Weather
Research and Forecasting (WRF) model when the available simulations are not
generated based on hierarchically nested experimental design. The proposed
procedure, called Augmented Bayesian Treed Co-Kriging, 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 non-stationary 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
non-hierarchically nested by enabling the specification of semi-conjugate
priors. Our imputation strategy allows the design of an efficient RJ-MCMC
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 a benchmark example, and compared
against existing methods. The proposed method is used for the analysis of a
large-scale climate modeling application which involves the WRF model.
