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Uncertainty Quantification in Case of Imperfect Models: A Non‐Bayesian Approach

Author

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  • Michael Kohler
  • Adam Krzyżak
  • Shashidhar Mallapur
  • Roland Platz

Abstract

The starting point in uncertainty quantification is a stochastic model, which is fitted to a technical system in a suitable way, and prediction of uncertainty is carried out within this stochastic model. In any application, such a model will not be perfect, so any uncertainty quantification from such a model has to take into account the inadequacy of the model. In this paper, we rigorously show how the observed data of the technical system can be used to build a conservative non‐asymptotic confidence interval on quantiles related to experiments with the technical system. The construction of this confidence interval is based on concentration inequalities and order statistics. An asymptotic bound on the length of this confidence interval is presented. Here we assume that engineers use more and more of their knowledge to build models with order of errors bounded by log(n)/n. The results are illustrated by applying the newly proposed approach to real and simulated data.

Suggested Citation

  • Michael Kohler & Adam Krzyżak & Shashidhar Mallapur & Roland Platz, 2018. "Uncertainty Quantification in Case of Imperfect Models: A Non‐Bayesian Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 729-752, September.
    • Handle: RePEc:bla:scjsta:v:45:y:2018:i:3:p:729-752
    DOI: 10.1111/sjos.12317
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    Cited by:

    1. Michael Kohler & Adam Krzyżak, 2020. "Estimating quantiles in imperfect simulation models using conditional density estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 123-155, February.
    2. Benedict Götz & Sebastian Kersting & Michael Kohler, 2021. "Estimation of an improved surrogate model in uncertainty quantification by neural networks," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(2), pages 249-281, April.

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