A Fast and Calibrated Computer Model Emulator: An Empirical Bayes Approach

• Activity Number: 104 - Advances in Bayesian Analysis of Computer Models
• Type: Topic Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Vojtech Kejzlar* and Mookyong Son and Shrijita Bhattacharya and Tapabrata Maiti
• Companies: Skidmore College and Michigan State University and Michigan State University and Michigan State University
• Keywords: Gaussian process; Nonparametric regression; Computer experiments; Posterior consistency; Nuclear binding energies

Abstract

Mathematical models implemented on a computer have become the driving force behind the acceleration of the cycle of scientific processes. This is because computer models are typically much faster and more economical to run than physical experiments. In this work, we develop an empirical Bayes approach to predictions of physical quantities using a computer model, where we assume that the computer model under consideration needs to be calibrated and is computationally expensive. We propose a Gaussian process emulator and a Gaussian process model for the systematic discrepancy between the computer model and the underlying physical process. This allows for closed-form and easy-to-compute predictions given by a conditional distribution induced by the Gaussian processes. We provide a rigorous theoretical justification of the proposed approach by establishing posterior consistency of the estimated physical process. The computational efficiency of the methods is demonstrated in an extensive simulation study and a real data example.