P-box papers

Introductions to probability boxes (p-boxes) and probability bounds analysis

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, Available on-line at http://www.ramas.com/unabridged.zip

Ferson, S., and J. Siegrist. 2012. Verified computation with probabilities. Pages 95-122 in Uncertainty Quantification in Scientific Computing, edited by A. Dienstfrey and R.F. Boisvert, Springer, New York. http://www.ramas.com/health/verifiedprob.pdf

Beer, M., S. Ferson, and V. Kreinovich. 2013. Imprecise probabilities in engineering analyses. Mechanical Systems and Signal Processing 37: 429. http://www.ramas.com/health/ip.pdf

Ferson, S., D.R.J. Moore, P. van der Brink, T.L. Estes, K. Gallagher, R. O’Connor and F. Verdonck. 2010. Bounding uncertainty analyses. Application of Uncertainty Analysis to Ecological Risks of Pesticides, edited by W. Warren-Hicks and A. Hart, SETAC Press, Pensacola, Florida

Early papers

Ferson, S. 1994. Naive Monte Carlo methods yield dangerous underestimates of tail probabilities. Proceedings of the High Consequence Operations Safety Symposium, Sandia National Laboratories, SAND94-2364, J.A. Cooper (ed.), pp. 507–514.

Ferson, S., L.R. Ginzburg, H.R. Akcakaya. 1995. Whereof one cannot speak: when input distributions are unknown. Applied Biomathematics technical report, http://www.ramas.com/whereof.pdf [this paper is often cited as "Risk Analysis (to appear)"]

Ferson, S., and T.F. Long. 1995. Conservative uncertainty propagation in environmental risk assessments. Environmental Toxicology and Risk Assessment, Third Volume, ASTM STP 1218, J.S. Hughes, G.R. Biddinger and E. Mones (eds.), American Society for Testing and Materials, Philadelphia, pp. 97–110.

Ferson, S. 1996. What Monte Carlo methods cannot do. Human and Ecological Risk Assessment 2:990–1007.

Ferson, S., and L.R. Ginzburg. 1996. Different methods are needed to propagate ignorance and variability. Reliability Engineering and Systems Safety 54:133–144. [This paper was identified as a “sleeping beauty” by Sarah Huggett in her article “‘Sleeping Beauties’ or delayed recognition: when old ideas are brought to bibliometric life” in Research Trends (January 2011, http://www.researchtrends.com/issue21-january-2011/%E2%80%9Csleeping-beauties%E2%80%9D-or-delayed-recognition-when-old-ideas-are-brought-to-bibliometric-life/) because it was originally sparsely cited but later became highly cited.]

Ferson, S., and T.F. Long. 1997. Deconvolution can reduce uncertainty in risk analyses. Risk Assessment: Measurement and Logic, M. Newman and C. Strojan (eds.), Ann Arbor Press.

Ferson, S. 1997. Probability bounds analysis software. Computing in Environmental Resource Management. Proceedings of the Conference, A. Gertler (ed.), Air and Waste Management Association and the U.S. Environmental Protection Agency, Pittsburgh, Pennsylvania. pp. 669–678

Commercial software supporting probability bounds analysis

Ferson, S. 2002. RAMAS Risk Calc 4.0 Software: Risk Assessment with Uncertain Numbers. Lewis Publishers, Boca Raton, Florida. Described at www.ramas.com/riskcalc.htm [reviewed by http://www.tomasoberg.com/pdf/sra_poster_2005.pdf]

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. Described at www.ramas.com/constructor.pdf

Modeling dependence and uncertainty about dependence

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, NM. www.ramas.com/depend.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

Ferson, S., and V. Kreinovich. 2006. Modeling correlation and dependence among intervals. REC 06 Reliable Engineering Computing, Savannah, Georgia. www.gtrep.gatech.edu/workshop/rec06/REC'06_Proceedings.pdf, R. Muhannah et al. (eds.). Available on-line at www.gtrep.gatech.edu/workshop/rec06/papers/Ferson_paper.pdf

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

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

Sensitivity analysis

Ferson, S., and W.T. Tucker. 2006. Sensitivity in Risk Analysis with Uncertain Numbers. Sandia National Laboratories, SAND2006-2801, Albuquerque, NM. www.ramas.com/sensanal.pdf

Ferson, S., and W.T. Tucker. 2006. Sensitivity analysis using probability bounding, Reliability Engineering and System Safety 91: 1435-1442

Uncertainty about model structure

Ferson, S. 2014. Model uncertainty in risk analysis. Proceedings of the 6^th International Workshop of Reliable Engineering Computing: Reliability and Computations of Infrastructures, 25–28 May 2014, IIT, Chicago, Illinois, pages 27–43. http://rec2014.iit.edu/papers/Paper_Ferson.pdf

Statistics for data sets that include intervals

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., and J. Siegrist. 2011. Statistical inference under two structurally different approaches to interval data. Pages 29-37 in Vulnerability, Uncertainty, and Risk: Analysis, Modeling, and Management, edited by B.M. Ayyub. ASCE, Reston, VA. http://www.ramas.com/health/two.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

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

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

Translating English-languages expressions such as “about 3.4” into uncertain numbers

Ferson, S., J. O'Rawe, A. Antonenko, J. Siegrist, J. Mickley, C. Luhmann, K. Sentz, A. Finkel. 2015. Natural language of uncertainty: numeric hedge words. International Journal of Approximate Reasoning 57: 19-39. http://www.ramas.com/health/hedges.pdf

Confidence boxes (p-box shaped estimators for constant parameters)

Ferson, S., J. O’Rawe and M. Balch. 2014. Computing with confidence: imprecise posteriors and predictive distributions. Proceedings of the International Conference on Vulnerability and Risk Analysis and Management and International Symposium on Uncertainty Modeling and Analyis. http://www.ramas.com/health/icvram2014.pdf

Ferson, S., M. Balch, K. Sentz, and J. Siegrist. 2013. Computing with confidence. Proceedings of the 8th International Symposium on Imprecise Probability: Theories and Applications, edited by F. Cozman, T. Denoeux, S. Destercke and T. Seidenfeld. SIPTA, Compiègne, France. http://www.ramas.com/health/cboxes.pdf

O'Rawe, J.A., S. Ferson and G.J. Lyon. 2015. Accounting for uncertainty in DNA sequencing data. Trends in Genetics 31: 61-66. DOI:http://dx.doi.org/10.1016/j.tig.2014.12.002)

Validation

Ferson, S., and W.L. Oberkampf. 2009. Validation of imprecise probability models. International Journal of Reliability and Safety 3(1/2/3): 3–22

Ferson, S., W.L. Oberkampf and L. Ginzburg. 2008. Validation of imprecise probabilistic models. Third International Workshop on Reliable Engineering Computing, Savannah Georgia. R. Muhannah et al. (eds.). http://www.gtsav.gatech.edu/workshop/rec08/documents/REC08_Paper_Ferson_000.pdf

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

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

Projecting probability boxes through nonlinear ordinary differential equations

Enszer, J.A., Y. Lin, S. Ferson, G.F. Corliss, and M.A. Stadtherr. 2011. Probability bounds analysis for nonlinear dynamic process models. AIChE [American Institute of Chemical Engineers] Journal 57: 404–422

Enszer, J.A., Y. Lin, S. Ferson, G.F. Corliss and M.A. Stadtherr. 2008. Propagating uncertainties in modeling nonlinear dynamic systems. Third International Workshop on Reliable Engineering Computing, Savannah Georgia. http://www.gtsav.gatech.edu/workshop/rec08/documents/REC08_Papper_Enszer.pdf

Examples and applications of probability bounds analysis

Regan, H.M., B.K. Hope and S. Ferson. 2002. Analysis and portrayal of uncertainty in a food web exposure model. Human and Ecological Risk Assessment 8: 1757-1777. [Named Best HERA Paper of the Year for 2002]

Bruns, M., C.J.J. Paredis, and S. Ferson. 2006. Computational methods for decision making based on imprecise information. Pages 341-368 in Proceedings of the NSF Workshop on Reliable Engineering Computing: Modeling Errors and Uncertainty in Engineering Computations, February 22-24, 2006, Savannah, Georgia, USA, R.L. Muhanna and R.L. Mullen (eds.), www.gtrep.gatech.edu/workshop/rec06/papers/Burns_paper.pdf [sic]

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

Ferson, S., and W.T. Tucker. 2004. Reliability of risk analyses for contaminated groundwater. Groundwater Quality Modeling and Management under Uncertainty, edited by Srikanta Mishra, American Society of Civil Engineers Reston, VA

Ferson, S. 2001. Probability bounds analysis solves the problem of incomplete specification in probabilistic risk and safety assessements. Risk-Based Decisionmaking in Water Resources IX, Y.Y. Haimes, D.A. Moser and E.Z. Stakhiv (eds.), American Society of Civil Engineers, Reston, Virginia, page 173-188

Regan, H.M., B.E. Sample and S. Ferson. 2002. Comparison of deterministic and probabilistic calculation of ecological soil screening levels. Environmental Toxicology and Chemistry 21: 882-890

Sentz, K., and S. Ferson. 2011. Probabilistic bounding analysis in the quantification of margins and uncertainties. Reliability and Engineering System Safety 96: 1126–1136

Other papers

See many more examples listed in the Wikipedia article for probability bounds analysis