Advertisement

Epistemic Uncertainties: Dealing with a Lack of Knowledge

  • Ryan G. McClarren
Chapter

Abstract

This chapter attempts to assess the impact of uncertainties that do not have a known distribution. In Sect. 12.1 we introduce a metric for evaluating the agreement between simulation and experiments. We then extend our focus to the case of agreement between experiment and simulation when there are calibration parameters in the simulation. We treat these cases using horsetail plots and p-boxes. To make a prediction on a new experiment, we can use the p-box to adjust a prediction, as shown in Sect. 12.4. Section 12.5 introduces Dempster-Shafer evidence theory for including expert judgment to construct p-boxes, followed by Sect. 12.6 where Kolomogorov-Smirnov confidence bounds are presented and Sect. 12.7 on Cauchy deviates.

References

  1. Agnesi M (1748) Instituzioni analitiche ad uso della gioventú italiana. Nella Regia-Ducal CorteGoogle Scholar
  2. Chowdhary K, Dupuis P (2013) Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification. ESAIM Math Model Numer Anal 47(3):635–662MathSciNetCrossRefGoogle Scholar
  3. Ferson S, Kreinovich V, Ginzburg L, Myers D, Sentz K (2003) Constructing probability boxes and dempster-shafer structures. Tech. Rep. SAND2002-4015, Sandia National LaboratoriesGoogle Scholar
  4. Ferson S, Kreinovich V, Hajagos J, Oberkampf W, Ginzburg L (2007) Experimental uncertainty estimation and statistics for data having interval uncertainty. Tech. Rep. SAND2007-0939, Sandia National LaboratoriesGoogle Scholar
  5. Kreinovich V, Ferson SA (2004) A new Cauchy-based black-box technique for uncertainty in risk analysis. Reliab Eng Syst Saf 85(1–3):267–279CrossRefGoogle Scholar
  6. Kreinovich V, Nguyen HT (2009) Towards intuitive understanding of the Cauchy deviate method for processing interval and fuzzy uncertainty. In: Proceedings of the 2015 conference of the international fuzzy systems association and the european society for fuzzy logic and technology conference, pp 1264–1269Google Scholar
  7. Kreinovich V, Beck J, Ferregut C, Sanchez A, Keller G, Averill M, Starks S (2004) Monte-Carlo-type techniques for processing interval uncertainty, and their engineering applications. In: Proceedings of the workshop on reliable engineering computing, pp 15–17Google Scholar
  8. Marsaglia G, Tsang WW, Wang J (2003) Evaluating Kolmogorov’s distribution. J Stat Softw 8(18):1–4.  https://doi.org/10.18637/jss.v008.i18 CrossRefGoogle Scholar
  9. Oberkampf WL, Roy CJ (2010) Verification and validation in scientific computing, 1st edn. Cambridge University Press, New YorkCrossRefGoogle Scholar
  10. Owhadi H, Scovel C, Sullivan TJ, McKerns M, Ortiz M (2013) Optimal uncertainty quantification. SIAM Rev 55(2):271–345MathSciNetCrossRefGoogle Scholar
  11. Owhadi H, Scovel C, Sullivan T (2015) Brittleness of Bayesian inference under finite information in a continuous world. Electron J Stat 9(1):1–79MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ryan G. McClarren
    • 1
  1. 1.Department of Aerospace and Mechanical EngineeringUniversity of Notre DameNotre DameUSA

Personalised recommendations