Semi-parametric adjustment to computer models

Abstract

Computer simulations are widely used in scientific exploration and engineering designs. However, computer outputs usually do not match the reality perfectly because the computer models are built under certain simplifications and approximations. When physical observations are also available, statistical methods can be applied to estimate the discrepancy between the computer output and the physical response. In this article, we propose a semi-parametric method for statistical adjustments to computer models. The proposed method is proven to enjoy nice theoretical properties. We use three numerical studies and a real example to examine the predictive performance of the proposed method. The results show that the proposed method outperforms existing methods.

Keywords:

• Computer experiments
• reproducing kernel Hilbert spaces
• prediction
• uncertainty quantification

2010 Mathematics Subject Classification:

• 60G15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

Note: τ is the standard deviation of the modified observations in (37(37) $y_m^p(\cdot )=y_r^p(\cdot )+\mathrm{\Delta },$(37) ).

Additional information

Funding

This work was supported by Division of Mathematical Sciences [1914636].