Distributional Sensitivity for Uncertainty Quantification

Distributional Sensitivity for Uncertainty Quantification

Year:    2011

Communications in Computational Physics, Vol. 10 (2011), Iss. 1 : pp. 140–160

Abstract

In this work we consider a general notion of distributional sensitivity, which measures the variation in solutions of a given physical/mathematical system with respect to the variation of probability distribution of the inputs. This is distinctively different from the classical sensitivity analysis, which studies the changes of solutions with respect to the values of the inputs. The general idea is measurement of sensitivity of outputs with respect to probability distributions, which is a well-studied concept in related disciplines. We adapt these ideas to present a quantitative framework in the context of uncertainty quantification for measuring such a kind of sensitivity and a set of efficient algorithms to approximate the distributional sensitivity numerically. A remarkable feature of the algorithms is that they do not incur additional computational effort in addition to a one-time stochastic solver. Therefore, an accurate stochastic computation with respect to a prior input distribution is needed only once, and the ensuing distributional sensitivity computation for different input distributions is a post-processing step. We prove that an accurate numerical model leads to accurate calculations of this sensitivity, which applies not just to slowly-converging Monte-Carlo estimates, but also to exponentially convergent spectral approximations. We provide computational examples to demonstrate the ease of applicability and verify the convergence claims.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.160210.300710a

Communications in Computational Physics, Vol. 10 (2011), Iss. 1 : pp. 140–160

Published online:    2011-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:   

  1. Recent Developments in Computational Approaches to Optimization under Uncertainty and Application in Process Systems Engineering

    Geletu, Abebe | Li, Pu

    ChemBioEng Reviews, Vol. 1 (2014), Iss. 4 P.170

    https://doi.org/10.1002/cben.201400013 [Citations: 13]
  2. Materials Discovery and Design

    Is Automated Materials Design and Discovery Possible?

    McKerns, Michael

    2018

    https://doi.org/10.1007/978-3-319-99465-9_2 [Citations: 0]
  3. Quantile-constrained Wasserstein projections for robust interpretability of numerical and machine learning models

    Il Idrissi, Marouane | Bousquet, Nicolas | Gamboa, Fabrice | Iooss, Bertrand | Loubes, Jean-Michel

    Electronic Journal of Statistics, Vol. 18 (2024), Iss. 2

    https://doi.org/10.1214/24-EJS2268 [Citations: 0]
  4. On Upper and Lower Bounds for Quantity of Interest in Problems Subject to Epistemic Uncertainty

    Li, Jing | Qi, Xin | Xiu, Dongbin

    SIAM Journal on Scientific Computing, Vol. 36 (2014), Iss. 2 P.A364

    https://doi.org/10.1137/120892969 [Citations: 6]
  5. Efficient computation of unsteady flow in complex river systems with uncertain inputs

    Gibson, Nathan L. | Gifford-Miears, Christopher | Leon, Arturo S. | Vasylkivska, Veronika S.

    International Journal of Computer Mathematics, Vol. 91 (2014), Iss. 4 P.781

    https://doi.org/10.1080/00207160.2013.854336 [Citations: 10]