On-going research on methods, tools, and case studies for handling epistemic and aleatory uncertainty, uncertainty analysis, and uncertainty quantification for engineered systems has produced a variety of scholarly papers, research presentations, and technical reports, including these freely available items:
Introduction to epistemic and aleatory uncertainty
report: Probability bounds analysis in environmental risk assessment
report: Uncertainty propagation
Probability boxes (p-boxes)
Dependencies and correlations
Statistics for data with interval uncertainty:
Calibration
[forthcoming] report: Calibration of computer models under uncertainty
Validation against empirical observations
Sensitivity analysis
[forthcoming] report: Sensitivity analysis for computer models
Aggregation (data fusion)
Nonlinear ordinary differential equations
Elicitation of probability distributions, p-boxes and Dempster−Shafer structures:
Dependencies among intervals
Miscellaneous
These products have been prepared as part of on-going research supported under various projects including “Development of Advanced Wings Solutions (DAWS)” funded by Innovate UK (46357), “Digital twins for improved dynamic design” funded by EPSRC (EP/R006768/1), “Epistemic uncertainty project”, funded by Sandia National Laboratories (contract number 19094), and, supporting the participation of graduate researchers, “Centre for Doctoral Training in Quantification and Management of Risk and Uncertainty in Complex Systems and Environments” jointly funded by EPSRC and ESRC (EP/L015927/1).
Below is a full list of the publications arising from or closely related to the Sandia project.
Helton, J.C., J.D. Johnson, W.L. Oberkampf and C.J. Sallaberry. 2010. Representation of analysis results involving aleatory and epistemic uncertainty. International Journal of General Systems 39(6): 605−646.
Ferson, S., and W.L. Oberkampf. 2009. Validation of imprecise probability models. International Journal of Reliability and Safety 3(1/2/3): 3–22.
Nguyen, H.T., O. Kosheleva, V. Kreinovich and S. Ferson. 2009. Trade-off between sample size and accuracy: case of measurements under interval uncertainty. International Journal of Approximate Reasoning 50: 1164−1176.
Helton, J.C., J.D. Johnson and W.L. Oberkampf. 2009. Effect of delayed link failure on probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links. Reliability Engineering and System Safety 94: 294−310.
Kreinovich, V., J.G. Hajagos, W.T. Tucker, J. Beck, L.R. Ginzburg and S. Ferson. 2008. Propagating Uncertainty through a Quadratic Response Surface Model. SAND2008-5983, Sandia National Laboratories, Albuquerque, New Mexico. http://www.ramas.com/quadratic.pdf.
Ferson, S. and W.T. Tucker. 2008. Probability boxes as info-gap models. Proceedings of the North American Fuzzy Information Processing Society, IEEE, New York City.
Longpré, L., S. Ferson, and W.T. Tucker. 2008. How to measure a degree of mismatch between probability models, p-boxes, etc.: a decision-theory-motivated utility-based approach. Proceedings of the North American Fuzzy Information Processing Society, IEEE, New York City.
Ferson, S., W.L. Oberkampf and L. Ginzburg. 2008. Validation of imprecise probability models. Pages 23−44 in Proceedings of the Third International Workshop on Reliable Engineering Computing, NSF Workshop on Imprecise Probability in Engineering Analysis and Design, edited by R.L. Muhanna and R.L. Mullen. Center for Reliable Engineering Computing (REC), Georgia Tech, Savannah, Georgia. Paper:http://savannah.gatech.edu/workshop/rec08/documents/REC08_Paper_Ferson_000.pdf. Powerpoint slides: http://savannah.gatech.edu/workshop/rec08/documents/validationrec08.ppt.
Oberkampf, W.L. and S. Ferson. 2008. Model validation under both aleatory and epistemic uncertainty. Proceedings of the Symposium on Computational Uncertainty in Military Vehicle Design, NATO/RTO Applied Vehicle Technology Panel, Athens, Greece.
Nguyen, H.T., O. Kosheleva, V. Kreinovich, and S. Ferson. 2008. Trade-off between sample size and accuracy: case of dynamic measurements under interval uncertainty. Pages 45−56 in Interval/Probabilistic Uncertainty and Non-classical Logics, V.-N. Huynh, Y. Nakamori, H. Ono, J. Lawry, V. Kreinovich and H.T. Nguyen (eds.), Springer, Berlin.
Enszer, J.A., Y. Lin, S. Ferson, G.F. Corliss, M.A. Stadtherr. 2008. Propagating uncertainties in modeling nonlinear dynamic systems. Pages 89−105 in Proceedings of the Third International Workshop on Reliable Engineering Computing, NSF Workshop on Imprecise Probability in Engineering Analysis and Design, edited by R.L. Muhanna and R.L. Mullen. Center for Reliable Engineering Computing (REC), Georgia Tech, Savannah, Georgia. Paper: http://savannah.gatech.edu/workshop/rec08/documents/REC08_Papper_Enszer.pdf. PDF slides: http://savannah.gatech.edu/workshop/rec08/documents/rec08_enszer_et_al.pdf.
Ferson, S., W.L. Oberkampf and L. Ginzburg. 2008. Model validation and predictive capability for the thermal challenge problem. Computer Methods in Applied Mechanics and Engineering 197: 2408−2430. Available at http://www.ramas.com/thermval.pdf.
Ferson, S., V. Kreinovich, J. Hajagos, W.L. Oberkampf and L. Ginzburg 2007. Experimental Uncertainty Estimation and Statistics for Data Having Interval Uncertainty. SAND2007-0939, Sandia National Laboratories, Albuquerque, New Mexico. http://www.ramas.com/intstats.pdf.
Ferson, S., L. Ginzburg, V. Kreinovich and J. Lopez. 2007. Absolute bounds on the mean of the sum, product, max, and min: a probabilistic extension of interval arithmetic. Applied Mathematical Sciences 1(9): 395−440.
Helton, J.C., J.D. Johnson and W.L. Oberkampf. 2007. Verification of the calculation of probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links. Reliability Engineering and System Safety 92: 1363−1373.
Helton, J.C., J.D. Johnson and W.L. Oberkampf. 2007. Verification test problems for the calculation of probability of loss of assured safety in temperature-dependent systems with multiple weak and strong links. Reliability Engineering and System Safety 92: 1374−1387.
Helton, J.C., J.D. Johnson, W.L. Oberkampf and C.B. Storlie. 2007. A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Computer Methods in Applied Mechanics and Engineering 196(37−40): 3980−3998.
Kreinovich, V., L. Longpré, S.A. Starks, G. Xiang, J. Beck, R. Kandathi, A. Nayak, S. Ferson and J. Hajagos. 2007. Interval versions of statistical techniques with applications to environmental analysis, bioinformatics, and privacy in statistical databases. Journal of Computational and Applied Mathematics 199(2): 418−423.
Ceberio, M., S. Ferson, V. Kreinovich, S. Chopra, G. Xiang, A. Murguia and J. Santillan. 2007. How to take into account dependence between the inputs. Journal of Uncertain Systems 1:14−37.
Ceberio, M., S. Ferson, V. Kreinovich, S. Chopra, G. Xiang, A. Murguia, J. Santillan. 2006. How to take into account dependence between the inputs: from interval computationsto constraint-related set computations, with potential applications to nuclear safety,bio- and geosciences. Pages 127−154 in Proceedings of the NSF Workshop on Reliable Engineering Computing: Modeling Errors and Uncertainty in Engineering Computations, edited by R.L. Muhanna and R.L. Mullen. Center for Reliable Engineering Computing (REC), Georgia Tech, Savannah, Georgia. Paper: http://savannah.gatech.edu/workshop/rec06/papers/Ceberio_paper.pdf, Slides: http://savannah.gatech.edu/workshop/rec06/presentations/REC2006_Kreinovich.pdf.
Ferson, S. and J.G. Hajagos. 2006. Varying correlation coefficients can underestimate uncertainty in probabilistic models. Reliability Engineering and System Safety 91: 1461−1467.
Kreinovich, V., G. Xiang and S. Ferson. 2006. Computing mean and variance under Dempster−Shafer uncertainty: towards faster algorithms. International Journal of Approximate Reasoning 42: 212−227.
Ferson, S. and W.T. Tucker. 2006. Sensitivity in Risk Analysis with Uncertain Numbers. Sandia National Laboratories, SAND2006-2801, Albuquerque, New Mexico. www.ramas.com/sensanal.pdf.
Ferson, S., and V. Kreinovich. 2006. Modeling correlations and dependencies among intervals. Pages 341−369 in Proceedings of the NSF Workshop on Reliable Engineering Computing: Modeling Errors and Uncertainty in Engineering Computations, edited by R.L. Muhanna and R.L. Mullen. Center for Reliable Engineering Computing (REC), Georgia Tech, Savannah, Georgia. Paper: http://savannah.gatech.edu/workshop/rec06/papers/Ferson_paper.pdf. Powerpoint slides: http://savannah.gatech.edu/workshop/rec06/presentations/REC2006_Ferson.ppt.
Ferson, S. and W.T. Tucker. 2006. Sensitivity analysis using probability bounding, Reliability Engineering and System Safety 91: 1435−144.
Kreinovich, V., and S. Ferson. 2006. Computing best-possible bounds for the distribution of a sum of several variables is NP-hard. International Journal of Approximate Reasoning 41: 331−342.
Helton, J.C., J.D. Johnson and W.L. Oberkampf. 2006. Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links. Reliability Engineering and System Safety 91(3): 320−348.
Helton, J.C., J.D. Johnson, W.L. Oberkampf and C.J. Sallaberry. 2006. Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty. Reliability Engineering and System Safety 91(10−11): 1414−1434.
Bruns, M., C.J.J. Paredis, and S. Ferson. 2006. Computational methods for decisionmaking based on imprecise information. Pages 341−368 in Proceedings of the NSF Workshop on Reliable Engineering Computing: Modeling Errors and Uncertainty in Engineering Computations, edited by R.L. Muhanna and R.L. Mullen. Center for Reliable Engineering Computing (REC), Georgia Tech, Savannah, Georgia. Paper: http://savannah.gatech.edu/workshop/rec06/papers/Burns_paper.pdf, Slides: http://savannah.gatech.edu/workshop/rec06/presentations/REC2006_Bruns.ppt.
Ferson, S. J. Hajagos, D.S. Meyers and W.T. Tucker. 2005. Constructor: Synthesizing Information about Uncertain Variables. Sandia National Laboratories, SAND2005-3769, Albuquerque, New Mexico, www.ramas.com/constructor.pdf.
Ferson, S., L. Ginzburg, V. Kreinovich, L. Longpré, and M. Aviles. 2005. Exact bounds on finite populations of interval data. Reliable Computing 11(3): 207−233.
Joslyn, C., and J. Booker. 2005. Generalized information theory for engineering modeling and simulation. Pages 1−40 in chapter 9 of Engineering Design Reliability Handbook, edited by E. Nikolaidis, D.M. Ghiocel, and S. Singhal, CRC Press, Boca Raton, Florida.
Joslyn, C., and V. Kreinovich. 2005. Convergence properties of an interval probabilistic approach to system reliability estimation. International Journal of General Systems 34(4): 465−482.
Ferson, S., V. Kreinovich, and W.T. Tucker. 2005. Untangling equations involving uncertainty. Presentation at the NSF workshop on Reliable Engineering Computing, September 15−17, 2004, Georgia Tech, Savannah, Georgia. Powerpoint slides: http://savannah.gatech.edu/workshop/rec04/presentations/Fearson.ppt.
Oberkampf, W.L. and J.C. Helton. 2005. Evidence theory for engineering applications. Engineering Design Reliability Handbook, edited by E. Nikolaidis, D.M. Ghiocel and S. Singhal. New York, CRC Press.
Helton, J.C., W.L. Oberkampf and J.D. Johnson. 2005. Competing failure risk analysis using evidence theory. Risk Analysis 25(4): 973−995.
Kreinovich, K., L. Longpré, P. Patangay, S. Ferson, and L. Ginzburg. 2005. Outlier detection under interval uncertainty: algorithmic solvability and computational complexity. Reliable Computing 11: 59−76.
Kreinovich, K., E.J. Pauwels, S. Ferson and L. Ginzburg. 2004. A feasible algorithm for locating concave and convex zones of interval data and its use in statistics-based clustering. Numerical Algorithms 37: 225−232.
Ferson, S., R. Nelsen, J. Hajagos, D. Berleant, J. Zhang, W.T. Tucker, L. Ginzburg and W.L. Oberkampf. 2004. Dependence in Probabilistic Modeling, Dempster−Shafer Theory, and Probability Bounds Analysis. Sandia National Laboratories, SAND2004-3072, Albuquerque, New Mexico. www.ramas.com/depend.pdf.
Ferson, S., W. Troy Tucker and W.L. Oberkampf. 2004. The notion of independence when probabilities are imprecise. 9th ASCE EMD/SEI/GI/AD Joint Specialty Conference on Probabilistic Mechanics and Structural Reliability (PMC2004), Albuquerque, New Mexico.
Ferson, S. and J. Hajagos. 2004. Arithmetic with uncertain numbers: rigorous and (often) best-possible answers. Reliability and Engineering and System Safety 85: 135−152.
Ferson, S., C.A. Joslyn, J.C. Helton, W.L. Oberkampf and K. Sentz. 2004. Summary from the epistemic uncertainty workshop: consensus amid diversity. Reliability and Engineering and System Safety 85: 355−370.
Oberkampf, W.L., J.C. Helton, C.A. Joslyn, S.F. Wojtkiewicz and S. Ferson. 2004. Challenge problems: uncertainty in system response given uncertain parameters. Reliability and Engineering and System Safety 85: 11−20.
Joslyn, C. and S. Ferson. 2004. Approximate representations of random intervals for hybrid uncertainty quantification in engineering modeling. Proceedings of the Fourth International Conference on Sensitivity Analysis of Model Output. Los Alamos National Laboratory, Los Alamos, NM.
Kreinovich, V. and S.A.[sic] Ferson. 2004. A new Cauchy-based black-box technique for uncertainty in risk analysis. Reliability and Engineering and System Safety 85: 267−280.
Helton, J.C. and W.L. Oberkampf. 2004. Guest editorial: alternative representations of epistemic uncertainty. Reliability Engineering and System Safety 85(1-3): 1−10.
Helton, J.C., J.D. Johnson and W.L. Oberkampf. 2004. An exploration of alternative approaches to the representation of uncertainty in model predictions. Reliability Engineering and System Safety 85(1-3): 39−71.
Helton, J.C., J.D. Johnson and W.L. Oberkampf. 2004. Probability of Loss of Assured Safety in Temperature Dependent Systemswith Multiple Weak and Strong Links. Sandia National Laboratories, SAND2004-5216, Albuquerque, NM.
Kreinovich, V., S. Ferson and L. Ginzburg. 2003. Exact upper bound on the mean of the product of many random variables with known expectations. Reliable Computing 9(6): 441−463.
Berleant, D., M.P. Cheong, C. Chu, Y. Guan, A. Kamal, G. Shebl, S. Ferson, and J.F. Peters. 2003. Dependable handling of uncertainty. Reliable Computing 9(6): 407−418.
Joslyn, C. 2003. Multi-interval elicitation of random intervals for engineering reliability analysis. Pages 168−173 in Fourth International Symposium on Uncertainty Modeling and Analysis (ISUMA 03), edited by B.M. Ayyub and N.O. Attoh-Okine. Institute of Electrical & Electronics Engineers.
Ferson, S., L.R. Ginzburg and H.R. Akçakaya. 2003. Whereof one cannot speak: when input distributions are unknown. http://www.ramas.com/whereof.pdf.
Ferson, S. and W.T. Tucker 2003. Reliability of risk analyses for contaminated groundwater. Groundwater Quality Modeling and Management Under Uncertainty, edited by S. Mishra, American Society of Civil Engineers, Reston, Virginia.
Ferson, S., V. Kreinovich, L. Ginzburg, K. Sentz and D.S. Myers. 2003. Constructing probability boxes and Dempster−Shafer structures. Sandia National Laboratories, SAND2002-4015, Albuquerque, New Mexico. http://www.ramas.com/unabridged.zip.
Helton, J.C., W.L. Oberkampf and J.D. Johnson. 2003. Competing failure risk analysis using evidence theory. Proceedings of the 5th AIAA Non-Deterministic Approaches Forum, Paper 2003-1911, Norfolk, VA, American Institute of Aeronautics and Astronautics.
Ferson, S., L. Ginzburg, V. Kreinovich, L. Longpré and M. Aviles. 2002. Computing variance for interval data is NP-hard. ACM SIGACT News 33(2): 108−118.
Joslyn, C., and J.C. Helton. 2002. Bounds on plausibility and belief of functionally propagated random sets. Pages 412−417 in Proceedings of the Conference of the North American Fuzzy Information Processing Society (NAFIPS 2002), 27−29 June 2002, New Orleans, Louisiana.
Joslyn, C., and W. Oberkampf. 2002. Uncertainty quantification of simulation codes using probability intervals. Poster at Workshop on Quantification of Uncertainty in Physics Simulations, 9−10 September 2002, Los Alamos National Laboratory, Los Alamos, New Mexico.
Sentz, K. and S. Ferson. 2002. Combination of Evidence in Dempster−ShaferTheory. Sandia National Laboratories, SAND 2002-0835, Albuquerque, New Mexico. http://www.sandia.gov/epistemic/Reports/SAND2002-0835.pdf.
Oberkampf, W.L., J.C. Helton and K. Sentz. 2001. Mathematical representation of uncertainty. Proceedings of the 3rd AIAA Non-Deterministic Approaches Forum, Paper 2001-1645, Seattle, WA, American Institute of Aeronautics and Astronautics.
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