Abstract
Quantification of uncertainty of a technical system is often based on a surrogate model of a corresponding simulation model. In any application the simulation model will not describe the reality perfectly, and consequently also the surrogate model will be imperfect. In this article we show how observed data of the real technical system can be used to improve such a surrogate model, and we analyze the rate of convergence of density estimates based on the improved surrogate model. The results are illustrated by applying the estimates to simulated and real data.
Highlights
Quantification of uncertainty of a technical system is often based on a surrogate model of a corresponding simulation model
In this article we show how observed data of the real technical system can be used to improve such a surrogate model, and we analyze the rate of convergence of density estimates based on the improved surrogate model
Any design of complex technical systems by engineers nowadays is based on some sort of mathematical model of the technical system
Summary
Any design of complex technical systems by engineers nowadays is based on some sort of mathematical model of the technical system. Tuo and Wu (2015) pointed out that this approach might lead to estimates, which are not consistent (in the sense introduced by them) in case of an imperfect computer model, for which there exist no values of the parameters which fit the technical system perfectly They suggested and analyzed non-Bayesian methods for the choice of parameters of such models. In this paper we are interested in a non-Bayesian approach towards uncertainty quantification in case of imperfect models Such an approach was proposed in Wong, Storlie and Lee (2017), where standard nonparametric regression estimates have been applied in order to estimate the discrepancy function between the model and the real data by using these methods to smooth the residuals of the model. Let D ⊆ Rd and let f : Rd → R be a real-valued function defined on Rd. The outline of this paper is as follows: In Section 2 the construction of the improved surrogate model is explained. The finite sample size performance of our estimates is illustrated in Section 4 by applying it to simulated and real data
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