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Uncertainty Quantification in Case of Imperfect Models: A Non‐Bayesian Approach
Author(s) -
Kohler Michael,
Krzyżak Adam,
Mallapur Shashidhar,
Platz Roland
Publication year - 2018
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12317
Subject(s) - mathematics , quantile , point estimation , uncertainty quantification , confidence interval , coverage probability , prediction interval , interval (graph theory) , bayesian probability , bounded function , imperfect , sensitivity analysis , stochastic modelling , order statistic , uncertainty analysis , statistics , mathematical analysis , linguistics , philosophy , combinatorics
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 l o g ( n ) / n . The results are illustrated by applying the newly proposed approach to real and simulated data.