A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory

Abstract

Prepared by Sandia Nat ional Labor at ori es Albu querque , Ne w Mexico 87185 and Livermore , Ca liforn ia 94550Sandia is a mult iprogr am laborat or y operated by Sandia Corpo ratio n, a Lockh eed Mar tin Compa ny, for th e United States Depa rt ment of Energy's National Nuclear Securi ty Admi nistration under Contract DE-A C04-94AL 85000 .App rov ed for public release; furth er dissemination unlimited . (rI1) Sandia National LaboratoriesIssued by Sandia National Laboratories, operated for the United States Department of Energy by Sandia Corporation. NOTICE:This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government, nor any agency thereof, nor any of their employees, nor any of their contractors, subcontractors, or their employees, make any warranty, express or implied, or assume any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represent that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government, any agency thereof, or any of their contractors or subcontractors. The views and opinions expressed herein do not necessarily state or reflect those of the United States Government, any agency thereof, or any of their contractors.Printed in the United States of America. This report has been reproduced directly from the best available copy. AbstractEvidence theory provides an alternative to probability theory for the representation of epistemic uncertainty in model predictions that derives from epistemic uncertainty in model inputs, where the descriptor epistemic is used to indicate uncertainty that derives from a lack of knowledge with respect to the appropriate values to use for various inputs to the model. The potential benefit, and hence appeal, of evidence theory is that it allows a less restrictive specification of uncertainty than is possible within the axiomatic structure on which probability theory is based. Unfortunately, the propagation of an evidence theory representation for uncertainty through a model is more computationally demanding than the propagation of a probabilistic representation for uncertainty, with this difficulty constituting a serious obstacle to the use of evidence theory in the representation of uncertainty in predictions obtained from computationally intensive models. This presentation describes and illustrates a samplingbased computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Preliminary trials indicate that the presented strategy can be used to propagate uncertainty representations based on evidence theory in analysis situations where naive sampling-based (i.e., unsophisticated Monte Carlo) procedures are impr...

A methodology for performing global uncertainty and sensitivity analysis in systems biology

“…This type of uncertainty is termed aleatory (or stochastic, irreducible, type A, see (Helton et al, 2006)). This distinction has been and still is an area of interest and study in the engineering and risk assessment community (see (Apostolakis, 1990;Helton, 1997;Helton et al, 2007;Parry & Winter, 1981;Pate'-Cornell, 1996)). …”

Sensitivity in risk analyses with uncertain numbers.

“…PBA and DST cannot be rigorously applied to black box models, at least with algorithms currently available. Various sampling schemes have been proposed to extend DST and PBA to black boxes (e.g., Helton et al 2004a,b;2006c;Bruns et al 2006), but, because they are necessarily approximation methods, they abandon the guarantee that the results will enclose the true distributions. This means that the sampling-based methods do not provide "automatic result verification" (sensu Adams and Kulisch 1993), although numerical simulations suggest that overall error rates can be made reasonably small if the black box permits many samples to be computed.…”

“…The approach is designed for problems involving Dempster-Shafer inputs, but it can be immediately applied to problems with p-boxes using the basic conversions described in Ferson et al (2003). In principle, various ancillary strategies might be used to accelerate the convergence of this approach, such as methods that take account of overlap among the input intervals or the likely association of extreme values of the output variables with extreme values of the input variables, or employ strategic simplifications to reduce the dimensionality of the problem (Helton et al 2006c). The approach was illustrated for a problem involving an algebraic expression in Helton et al (2004b), and for a much more complex problem involving competing failure risks of strong and weak switches in Helton et al (2004a).…”

Evaluation of risk from acts of terrorism :the adversary/defender model using belief and fuzzy sets.

“…[Ferson] Helton is developing Monte-Carlo sampling techniques for the belief/plausibility measure; such techniques would eliminate the dependence problem associated with repeated variables that cannot be factored. [Helton et al 2006] Also, as is the case for large-scale probabilistic evaluations, Monte-Carlo sampling would greatly improve the automation of the calculation of belief/plausibility.…”