Bayesian Additive Regression Tree Calibration of Complex High-Dimensional Computer Models

Complex natural phenomena are increasingly investigated by the use of a complex computer simulator. In order to leverage the advantages of simulators, observational data needs to be incorporated in a probabilistic framework so that uncertainties can be quantified. A popular framework for such experiments is the statistical computer model calibration experiment. A limitation often encountered in current statistical approaches for such experiments is the difficulty in modeling high dimensional observational datasets and simulator outputs as well as high-dimensional inputs. As the complexity of simulators seems to only grow, this challenge will continue unabated. In this paper, we develop a Bayesian statistical calibration approach that is ideally suited for such challenging calibration problems. Our approach leverages recent ideas from Bayesian Additive Regression Tree models to construct a random basis representation of the simulator outputs and observational data. The approach can flexibly handle high-dimensional datasets, high-dimensional simulator inputs and calibration parameters while quantifying important sources of uncertainty in the resulting inference. We demonstrate our methodology on a CO2 emissions rate calibration problem, and on a complex simulator of subterranean radionuclide dispersion, which simulates the spatial-temporal diffusion of radionuclides released during nuclear bomb tests at the Nevada Test Site. Supplementary computer code and datasets are available online.