# An improved approach to Bayesian computer model calibration and prediction

**Authors:** Mengyang Gu, Long Wang  
**arXiv:** [1707.08215](https://arxiv.org/abs/1707.08215)  
**Date:** 2017-07-25  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/1707.08215v1/

## Key points

- In the field of calibrating inexact computer models using experimental data:
- Inclusion of a discrepancy function modeled via a Gaussian stochastic process (GaSP) is standard practice.
- Challenges arise when calibration parameters are unidentifiable within the GaSP framework, leading to poor fits with experimental data.
- Mengyang Gu and Long Wang propose the scaled Gaussian stochastic process (S-GaSP):
- Serves as a bridge between $L_2$ calibration and GaSP calibration techniques.
- Offers a computationally feasible solution under the Bayesian paradigm.
- Enhances predictive capabilities regardless of the specific discrepancy function used.
- Aims to overcome limitations in existing methods and improve overall model performance.
- Numerical examples demonstrate the effectiveness of the S-GaSP model and highlight its differences from previous approaches.

## Summary

In the field of calibrating inexact computer models using experimental data, the inclusion of a discrepancy function modeled via a Gaussian stochastic process (GaSP) has become standard practice to improve prediction accuracy. However, challenges arise when the calibration parameters in the computer model are unidentifiable within the GaSP framework, resulting in poor fits with experimental data. To address this issue, Mengyang Gu and Long Wang propose a novel approach known as the scaled Gaussian stochastic process (S-GaSP). This innovative method serves as a bridge between two established calibration techniques - $L_2$ calibration and GaSP calibration - offering a computationally feasible solution under the Bayesian paradigm. The S-GaSP model provides a general framework for calibration that enhances predictive capabilities regardless of the specific discrepancy function employed. By introducing this new stochastic process, Gu and Wang aim to overcome limitations present in existing methods and improve overall model performance. Numerical examples are presented to demonstrate the effectiveness of the S-GaSP model and highlight its differences from previous approaches. Through their research, Gu and Wang contribute valuable insights to the field of Bayesian computer model calibration and prediction, offering a promising avenue for future advancements in this area of study.