Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy

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

<div><p>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.</p></div