Variational inference with vine copulas: an efficient approach for Bayesian computer model calibration

Abstract

With the advancements of computer architectures, the use of computational models proliferates to solve complex problems in many scientific applications such as nuclear physics and climate research. However, the potential of such models is often hindered because they tend to be computationally expensive and consequently ill-fitting for uncertainty quantification. Furthermore, they are usually not calibrated with real-time observations. We develop a computationally efficient algorithm based on variational Bayes inference (VBI) for calibration of computer models with Gaussian processes. Unfortunately, the standard fast-to-compute gradient estimates based on subsampling are biased under the calibration framework due to the conditionally dependent data which diminishes the efficiency of VBI. In this work, we adopt a pairwise decomposition of the data likelihood using vine copulas that separate the information on dependence structure in data from their marginal distributions and leads to computationally efficient gradient estimates that are unbiased and thus scalable calibration. We provide an empirical evidence for the computational scalability of our methodology together with average case analysis and describe all the necessary details for an efficient implementation of the proposed algorithm. We also demonstrate the opportunities given by our method for practitioners on a real data example through calibration of the Liquid Drop Model of nuclear binding energies.