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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
Abstract #322963
Title: A Fast and Calibrated Computer Model Emulator: An Empirical Bayes Approach
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

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.

Authors who are presenting talks have a * after their name.

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