Statistical foundation of variational Bayes computer models

Computer models are used to solve complex problems in many scientific applications, such as nuclear physics and climate research. Markov chain Monte Carlo-based Bayesian calibration of computer models although a popular approach, is computationally expensive. This work proposes a fast and scalable posterior approximation algorithm for Bayesian computer model calibration via Variational Inference. We provide the statistical guarantee ofthe proposed algorithm in the form of a posterior contraction theorem for the estimated physical process. To this end, we establish that the variational posterior concentrates in ϵn neighbourhoods of the true physical process under regularity assumptions on the variational family. The main results are shown in the two widely used classes of Gaussian process priors, the Squared Exponential covariance class and the Matérn covariance class. Finally, we provide a simulation study to demonstrate the proposed method’s computational efficiency and fidelity compared to the standard Markov chain MonteCarlo method.