Representation of analysis results involving aleatory and epistemic uncertainty

References

• Agro , K.E. 1997 . Sensitivity analysis in health economic and pharmacoeconomic studies: an appraisal of the literature . Pharmacoeconomics , 11 : 75 – 88 .
   PubMed Web of Science ®Google Scholar
• Ahn , K.-L. , Yang , J.-E. and Ha , J. 2006 . Formal qualification of the various sources of an uncertainty employed in the level 2 PSA and the underlying issues . Annals of nuclear energy , 33 : 878 – 893 .
   Web of Science ®Google Scholar
• Allen , M.R. 2000 . Quantifying the uncertainty in forecasts of anthropogenic climate change . Nature , 407 : 617 – 620 .
   PubMed Web of Science ®Google Scholar
• Apostolakis , G. 1990 . The concept of probability in safety assessments of technological systems . Science , 250 : 1359 – 1364 .
   PubMed Web of Science ®Google Scholar
• Ash , R.B. and Doléans-Dade , C.A. 2000 . Probability and measure theory , 2nd ed. , New York : Harcourt/Academic Press .
   Google Scholar
• Ayyub , B.M. 2001 . Elicitation of expert opinions for uncertainty and risks , Boca Raton, FL : CRC Press .
   Google Scholar
• Babendreier , J.E. and Castleton , K.J. 2005 . Investigating uncertainty and sensitivity in integrated, multimedia environmental models: tools for FRAMES-3MRA . Environmental modelling & software , 20 : 1043 – 1055 .
   Web of Science ®Google Scholar
• Bankes , S.C. 2002 . Tools and techniques for developing policies for complex and uncertain systems . Proceedings of the national academy of sciences of the United States of America , 99 : 7263 – 7266 .
   PubMed Web of Science ®Google Scholar
• Bardossy , A. and Duckstein , L. 1995 . Fuzzy rule-based modeling with applications to geophysical, biological and engineering systems , Boca Raton, FL : CRC Press .
   Google Scholar
• Bardossy , G. and Fodor , J. 2004 . Evaluation of uncertainties and risks in geology , New York : Springer-Verlag .
   Google Scholar
• Barry , T.M. 1996 . Recommendations on the testing and use of pseudo-random number generators used in Monte Carlo analysis for risk assessment . Risk analysis , 16 : 93 – 105 .
   Web of Science ®Google Scholar
• Bates , S.C. , Cullen , A. and Raftery , A.E. 2003 . Bayesian uncertainty assessment in multicompartment deterministic simulation models for environmental risk assessment . Environmetrics , 14 : 355 – 371 .
   Web of Science ®Google Scholar
• Baudrit , C. and Dubois , D. 2006 . Practical representations of incomplete probabilistic knowledge . Computational statistics & data analysis , 51 : 86 – 108 .
   Web of Science ®Google Scholar
• Billingsley , P. 1995 . Probability and measure , 3rd ed. , New York : Wiley .
   Google Scholar
• Borgonovo , E. and Peccati , L. 2006 . Uncertainty and global sensitivity analysis in the evaluation of investment projects . International journal of production economics , 104 : 62 – 73 .
   Web of Science ®Google Scholar
• Bowman , A.W. and Azzalini , A. 1997 . Applied smoothing techniques for data analysis , Oxford : Clarendon .
   Google Scholar
• Breeding , R.J. 1992 . Summary description of the methods used in the probabilistic risk assessments for NUREG-1150 . Nuclear engineering and design , 135 : 1 – 27 .
   Web of Science ®Google Scholar
• Briggs , A.H. 2000 . Handling uncertainty in cost-effectiveness models . Pharmacoeconomics , 17 : 479 – 500 .
   PubMed Web of Science ®Google Scholar
• Budnitz , R.J. 1998 . Use of technical expert panels: applications to probabilistic seismic hazard analysis . Risk analysis , 18 : 463 – 469 .
   Web of Science ®Google Scholar
• Cacuci , D.G. and Ionescu-Bujor , M. 2004 . A comparative review of sensitivity and uncertainty analysis of large-scale systems–II: statistical methods . Nuclear science and engineering , 147 : 204 – 217 .
   Web of Science ®Google Scholar
• Casman , E.A. , Morgan , M.G. and Dowlatabadi , H. 1999 . Mixed levels of uncertainty in complex policy models . Risk analysis , 19 : 33 – 42 .
   Web of Science ®Google Scholar
• Chaudhuri , P. 1994 . Piecewise polynomial regression trees . Statistica Sinica , 4 : 143 – 167 .
   Web of Science ®Google Scholar
• Cheeseman , P. 1988 . An inquiry into computer understanding . Computational intelligence , 4 : 58 – 66 .
   Google Scholar
• Cheok , M.C. , Parry , G.W. and Sherry , R.R. 1998 . Use of importance measures in risk-informed regulatory applications . Reliability engineering and system safety , 60 : 213 – 226 .
   Web of Science ®Google Scholar
• Chhibber , S. , Apostolakis , G. and Okrent , D. 1992 . A taxonomy of issues related to the use of expert judgments in probabilistic safety studies . Reliability engineering and system safety , 38 : 27 – 45 .
   Web of Science ®Google Scholar
• Christie , M.A. 2005 . Error analysis and simulations of complex phenomena . Los Alamos science , 29 : 6 – 25 .
   Google Scholar
• Cooke , R. 1991 . Experts in uncertainty: opinion and subjective probability in science , Oxford; New York : Oxford University Press .
   Google Scholar
• Cooke , R.M. and Goossens , L.H.J. 2004 . Expert judgement elicitation for risk assessment of critical infrastructures . Journal of risk research , 7 : 643 – 656 .
   Web of Science ®Google Scholar
• Cullen , A. 1999 . Addressing uncertainty-lessons from probabilistic exposure analysis . Inhalation toxicology , 11 : 603 – 610 .
   PubMed Web of Science ®Google Scholar
• D'Antonio , P.E. 1998 . “ Surety principles development and integration for nuclear weapons ” . In High consequence operations safety symposium II, SAND98-1557 , Edited by: Isbell , D. 141 – 149 . Albuquerque, NM : Sandia National Laboratories .
   Google Scholar
• DeCooman , G. 1997 . Possibility theory part I: measure- and integral-theoretic ground-work; part II: conditional possibility; part III: possibilistic independence . International journal of general systems , 25 : 291 – 371 .
   Web of Science ®Google Scholar
• DeCooman , G. , Ruan , D. and Kerre , E.E. , eds. 1995 . Foundations and applications of possibility theory, proceedings of FAPT ’95, Ghent, Belgium, 13-15 December, 1995 , River Edge, NJ : World Scientific Publishing Co .
   Google Scholar
• Demmie , P.N. 1998 . “ A first-principle based approach to quantitative assessment of nuclear-detonation safety ” . In High consequence operations safety symposium II, SAND98-1557 , Edited by: Isbell , D. 325 – 341 . Albuquerque, NM : Sandia National Laboratories .
   Google Scholar
• Dempster , A.P. 1967a . Upper and lower probabilities induced by a multivalued mapping . Annals of mathematical statistics , 38 : 325 – 339 .
   Google Scholar
• Dempster , A.P. 1967b . Upper and lower probability inferences based on a sample from a finite univariate population . Biometrika , 54 : 515 – 528 .
   PubMed Web of Science ®Google Scholar
• Dempster , A.P. 1968 . A generalization of bayesian inference . Journal of the royal statistical society, series B , 30 : 205 – 247 .
   Google Scholar
• Devolder , B. 2002 . Uncertainty quantification for multiscale simulations . Journal of fluids engineering , 124 : 29 – 41 .
   Web of Science ®Google Scholar
• Draper , D. 1995 . Assessment and propagation of model uncertainty . Journal of the royal statistical society, series B , 57 : 45 – 97 .
   Google Scholar
• Dubois , D. 2006 . Possibility theory and statistical reasoning . Computational statistics & data analysis , 51 : 47 – 69 .
   Web of Science ®Google Scholar
• Dubois , D. and Prade , H. 1980 . Fuzzy sets and systems: theory and applications , New York : Academic Press .
   Google Scholar
• Dubois , D. and Prade , H. 1988 . Possibility theory: an approach to computerized processing of uncertainty , New York : Plenum .
   Google Scholar
• Dubois , D. and Prade , H. 1989 . Fuzzy sets, probability and measurement . European journal of operational research , 40 : 135 – 154 .
   Web of Science ®Google Scholar
• Dubois , D. and Prade , H. 1998 . “ Possibility theory: qualitative and quantitative aspects ” . In Handbook of defeasible reasoning and uncertainty management systems , Edited by: Grabbay , D.M. and Smets , P. Vol. 1 , 169 – 226 . Boston, MA : Kluwer Academic Publishers .
   Google Scholar
• Dubois , D. and Prade , H. 2006 . Possibility theory and its applications: a retrospective and prospective view . CISM courses and lectures , 482 : 89 – 109 .
   Google Scholar
• Dubois , D. , Nguyen , H.T. and Prade , H. 2000 . “ Possibility theory, probability theory and fuzzy sets: misunderstandings, bridges and gaps ” . In Fundamentals of fuzzy sets , Edited by: Dubois , D. and Prade , H. 343 – 438 . Boston, MA : Kluwer Academic Publishers .
   Google Scholar
• Evans , J.S. 1994 . Use of probabilistic expert judgement in uncertainty analysis of carcinogenic potency . Regulatory toxicology and pharmacology , 20 : 15 – 36 .
   PubMed Web of Science ®Google Scholar
• Feller , W. 1971 . An introduction to probability theory and its applications , 2nd ed. , Vol. 2 , New York : Wiley .
   Google Scholar
• Ferson , S. and Ginzburg , L. 1996 . Different methods are needed to propagate ignorance and variability . Reliability engineering and system safety , 54 : 133 – 144 .
   Web of Science ®Google Scholar
• Ferson , S. and Tucker , W.T. 2006 . Sensitivity in risk analyses with uncertain numbers , Albuquerque, NM : Sandia National Laboratories, SAND2006-2801 .
   Google Scholar
• Fine , T.L. 1973 . Theories of probability: an examination of foundations , New York : Academic Press .
   Google Scholar
• Fishman , G.S. 1996 . Monte Carlo: concepts, algorithms, and applications , New York : Springer-Verlag .
   Google Scholar
• Frey , H.C. and Patil , S.R. 2002 . Identification and review of sensitivity analysis methods . Risk analysis , 22 : 553 – 578 .
   PubMed Web of Science ®Google Scholar
• Friedman , J.H. 1991 . Multivariate adaptive regression splines (with discussion) . The annals of statistics , 19 : 1 – 141 .
   Web of Science ®Google Scholar
• Garthwaite , P.H. , Kadane , J.B. and O'Hagan , A. 2005 . Statistical methods for eliciting probability distributions . Journal of the American statistical association , 100 : 680 – 700 .
   Web of Science ®Google Scholar
• Ghosh , S.T. and Apostolakis , G.E. 2006 . Extracting risk insights from performance assessments for high-level radioactive waste repositories . Nuclear technology , 153 : 70 – 88 .
   Web of Science ®Google Scholar
• Glimm , J. and Sharp , D.H. 1998 . Stochastic methods for the prediction of complex multiscale phenomena . Quarterly of applied mathematics , 56 : 741 – 765 .
   Web of Science ®Google Scholar
• Glimm , J. and Sharp , D.H. 1999 . Prediction and the quantification of uncertainty . Physica D , 133 : 152 – 170 .
   Web of Science ®Google Scholar
• Glynn , P.W. and Iglehart , D.L. 1989 . Importance sampling for stochastic simulations . Management science , 35 : 1367 – 1392 .
   Web of Science ®Google Scholar
• Goyal , A. 1992 . A unified framework for simulating markovian models of highly dependable systems . IEEE transactions on computers , 41 : 36 – 51 .
   Web of Science ®Google Scholar
• Guan , J.W. and Bell , D.A. 1991 . Evidence theory and its applications , Vols. 1, 2 , New York : North-Holland .
   Google Scholar
• Hacking , I. 1975 . The emergence of probability: a philosophical study of early ideas about probability, induction and statistical inference , London; New York : Cambridge University Press .
   Google Scholar
• Hacking , I. 2001 . An introduction to probability and inductive logic , Cambridge, New York : Cambridge University Press .
   Google Scholar
• Hall , J.W. and Lawry , J. 2001 . “ Imprecise probabilities of engineering system failure from random and fuzzy set reliability analysis ” . In Proc. 2nd International Symposium on Imprecise Probabilities and their Application , Edited by: de Cooman , G. , Fine , T.L. and Seidenfeld , T. 195 – 204 . Maastricht : Shaker Publishing . In
   Google Scholar
• Halpern , J.Y. and Fagin , R. 1992 . Two views of belief: belief as generalized probability and belief as evidence . Artificial intelligence , 54 : 275 – 317 .
   Web of Science ®Google Scholar
• Hamby , D.M. 1994 . A review of techniques for parameter sensitivity analysis of environmental models . Environmental monitoring and assessment , 32 : 135 – 154 .
   PubMed Web of Science ®Google Scholar
• Hammer , R. 1993 . Numerical toolbox for verified computing. I. basic numerical problems , New York : Springer Verlag .
   Google Scholar
• Harris , J.W. and Stocker , H. 1998 . Handbook of mathematics and computational science , New York : Springer-Verlag .
   Google Scholar
• Hastie , T.J. and Tibshirani , R.J. 1990 . Generalized additive models , London : Chapman & Hall .
   Google Scholar
• Heidelberger , P. 1995 . Fast simulation of rare events in queueing and reliability models . ACM transactions on modeling and computer simulation , 5 : 43 – 85 .
   Google Scholar
• Helton , J.C. 1993 . Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal . Reliability engineering and system safety , 42 : 327 – 367 .
   Web of Science ®Google Scholar
• Helton , J.C. 1994 . Treatment of uncertainty in performance assessments for complex systems . Risk analysis , 14 : 483 – 511 .
   Web of Science ®Google Scholar
• Helton , J.C. 1996 . Probability, conditional probability and complementary cumulative distribution functions in performance assessment for radioactive waste disposal . Reliability engineering and system safety , 54 : 145 – 163 .
   Web of Science ®Google Scholar
• Helton , J.C. 1997 . Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty . Journal of statistical computation and simulation , 57 : 3 – 76 .
   Web of Science ®Google Scholar
• Helton , J.C. 2003 . “ Mathematical and numerical approaches in performance assessment for radioactive waste disposal: dealing with uncertainty ” . In Modelling radioactivity in the environment , Edited by: Scott , E.M. 353 – 390 . New York : Elsevier Science .
   Google Scholar
• Helton , J.C. and Breeding , R.J. 1993 . Calculation of reactor accident safety goals . Reliability engineering and system safety , 39 : 129 – 158 .
   Web of Science ®Google Scholar
• Helton , J.C. and Burmaster , D.E. 1996 . Guest editorial: treatment of aleatory and epistemic uncertainty in performance assessments for complex systems . Reliability engineering and system safety , 54 : 91 – 94 .
   Web of Science ®Google Scholar
• Helton , J.C. and Davis , F.J. 2002 . Illustration of sampling-based methods for uncertainty and sensitivity analysis . Risk analysis , 22 : 591 – 622 .
   PubMed Web of Science ®Google Scholar
• Helton , J.C. and Davis , F.J. 2003 . Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems . Reliability engineering and system safety , 81 : 23 – 69 .
   Web of Science ®Google Scholar
• Helton , J.C. and Marietta , M.G. 2000 . Special issue: the 1996 performance assessment for the Waste Isolation Pilot Plant . Reliability engineering and system safety , 69 : 1 – 451 . guest eds
   Web of Science ®Google Scholar
• Helton , J.C. 2000 . Conceptual structure of the 1996 performance assessment for the Waste Isolation Pilot Plant . Reliability engineering and system safety , 69 : 151 – 165 .
   Web of Science ®Google Scholar
• Helton , J.C. , Johnson , J.D. and Oberkampf , W.L. 2004 . An exploration of alternative approaches to the representation of uncertainty in model predictions . Reliability engineering and system safety , 85 : 39 – 71 .
   Web of Science ®Google Scholar
• Helton , J.C. , Johnson , J.D. and Oberkampf , W.L. 2006a . Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links . Reliability engineering and system safety , 91 : 320 – 348 .
   Web of Science ®Google Scholar
• Helton , J.C. 2006b . Survey of sampling-based methods for uncertainty and sensitivity analysis . Reliability engineering and system safety , 91 : 1175 – 1209 .
   Web of Science ®Google Scholar
• Helton , J.C. 2007 . A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory . Computational methods in applied mechanics and engineering , 196 : 3980 – 3998 .
   Web of Science ®Google Scholar
• Hoffman , F.O. and Hammonds , J.S. 1994 . Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability . Risk analysis , 14 : 707 – 712 .
   PubMed Web of Science ®Google Scholar
• Hora , S.C. and Iman , R.L. 1989 . Expert Opinion in risk analysis: the NUREG-1150 methodology . Nuclear science and engineering , 102 : 323 – 331 .
   Web of Science ®Google Scholar
• Howson , C. and Urbach , P. 1993 . Scientific reasoning: the Bayesian approach , 2nd ed. , Chicago, IL : Open Court .
   Google Scholar
• Hussaarts , M. 2000 . “ The probabilistic optimisation of revetment on the dikes along the Frisian coast ” . In Coastal structures ’99 , Edited by: Losada , M. 325 – 329 . Rotterdam : Balkema .
   Google Scholar
• Iman , R.L. 1992 . “ Uncertainty and sensitivity analysis for computer modeling applications ” . In Reliability technology - 1992, The winter annual meeting of the american society of mechanical engineers, Anaheim, California, November 8-13, 1992 , Edited by: Cruse , T.A. 153 – 168 . New York : American Society of Mechanical Engineers, Aerospace Division .
   Google Scholar
• Ionescu-Bujor , M. and Cacuci , D.G. 2004 . A comparative review of sensitivity and uncertainty analysis of large-scale systems–I: deterministic methods . Nuclear science and engineering , 147 : 189 – 2003 .
   Web of Science ®Google Scholar
• Jaulin , L. 2001 . Applied interval analysis , New York : Springer-Verlag .
   Google Scholar
• Johnson , N.L. and Katz , S. 1970 . Continuous univariate distributions , Vol. 1 , New York : Wiley .
   Google Scholar
• Joslyn , C. and Helton , J.C. 2002 . “ Bounds on belief and plausibility of functionally propagated random sets ” . In 2002 Annual meeting of the north american fuzzy information processing society proceedings , Edited by: Keller , J. and Nasraoui , O. 412 – 417 . Piscataway, NJ : IEEE .
   Google Scholar
• Joslyn , C. and Kreinovich , V. 2005 . Convergence properties of an interval probabilistic approach to system reliability estimation . International journal of general systems , 34 : 465 – 482 .
   Web of Science ®Google Scholar
• Kallenberg , O. 2000 . Foundations of modern probability , 2nd ed. , New York : Springer-Verlag .
   Google Scholar
• Kann , A. and Weyant , J.P. 2000 . Approaches for performing uncertainty analysis in large-scale energy/economic policy models . Environmental modeling and assessment , 5 : 29 – 46 .
   Web of Science ®Google Scholar
• Kaplan , S. and Garrick , B.J. 1981 . On the quantitative definition of risk . Risk analysis , 1 : 11 – 27 .
   Google Scholar
• Katz , R.W. 2002 . Techniques for estimating uncertainty in climate change scenarios and impact studies . Climate research , 20 : 167 – 185 .
   Web of Science ®Google Scholar
• Kearfott , R.B. and Kreinovich , V. 1996 . Applications of interval computations , Boston, MA : Kluwer Academic Publishers .
   Google Scholar
• Keeney , R.L. and Winterfeldt , D.V. 1991 . Eliciting probabilities from experts in complex technical problems . IEEE transactions on engineering management , 38 : 191 – 201 .
   Web of Science ®Google Scholar
• Kelly , E.J. and Campbell , K. 2000 . Separating variability and uncertainty in environmental risk assessment - making choices . Human and ecological risk assessment , 6 : 1 – 13 .
   Web of Science ®Google Scholar
• Kennedy , M.C. 2006 . Case studies in Gaussian process modelling of computer codes . Reliability engineering and system safety , 91 : 1301 – 1309 .
   Web of Science ®Google Scholar
• Khatib-Rahbar , M. 1996 . Insights and comparisons of the level-2 results of recent probabilistic safety analyses . Nuclear engineering and design , 162 : 175 – 203 .
   Web of Science ®Google Scholar
• Kleijnen , J.P.C. and Helton , J.C. 1999 . Statistical analyses of scatterplots to identify important factors in large-scale simulations, 1: review and comparison of techniques . Reliability engineering and system safety , 65 : 147 – 185 .
   Web of Science ®Google Scholar
• Klir , G.J. 1989 . Is there more to uncertainty than some probability theorists might have us believe? . International journal of general systems , 15 : 347 – 378 .
   Web of Science ®Google Scholar
• Klir , G.J. 1994 . On the alleged superiority of probability representation of uncertainty . IEEE transactions on fuzzy systems , 2 : 27 – 31 .
   Web of Science ®Google Scholar
• Klir , G.J. 2000 . “ Measures of uncertainty and information ” . In Fundamentals of fuzzy sets , Edited by: Dubois , D. and Prade , H. 439 – 457 . Boston, MA : Kluwer Academic Publishers .
   Google Scholar
• Klir , G.J. and Wierman , M.J. 1999 . Uncertainty-based information , New York : Physica-Verlag .
   Google Scholar
• Kosko , B. 1990 . Fuzziness vs. probability . International journal of general systems , 17 : 211 – 240 .
   Web of Science ®Google Scholar
• L'Ecuyer , P. 1998 . “ Random number generation ” . In Handbook of simulation: principles, methodology, advances, applications, and practice , Edited by: Banks , J. 93 – 137 . New York : Wiley .
   Google Scholar
• Laskey , K.B. 1996 . Model uncertainty: theory and practical implications . IEEE transactions on systems, man, and cybernetics–part A: systems and humans , 26 : 340 – 348 .
   PubMed Web of Science ®Google Scholar
• Laviolette , M. and Seaman , J. 1992 . Evaluating fuzzy representations of uncertainty . Mathematical science , 17 : 26 – 41 .
   Google Scholar
• Laviolette , M. 1995 . A probabilistic and statistical view of fuzzy methods . Technometrics , 37 : 249 – 292 .
   Web of Science ®Google Scholar
• Li , H. and Wu , J. 2006 . “ Uncertainty analysis in ecological issues: an overview ” . In Scaling and uncertainty analysis in ecology: methods and applications , Edited by: Wu , J. , Jones , K.B. , Li , H. and Loucks , O.L. 45 – 66 . New York : Springer .
   Google Scholar
• Lindley , D.V. 1982 . Scoring rules and the inevitability of probability . International statistical review , 50 : 1 – 26 .
   Web of Science ®Google Scholar
• Lindley , D.V. 1987 . The probability approach to the treatment of uncertainty in artificial intelligence and expert systems . Statistical science , 2 : 17 – 24 .
   Google Scholar
• Long , J.C.S. and Ewing , R.C. 2004 . Yucca Mountain: earth-science issues at a geologic repository for high-level nuclear waste . Annual review of earth and planetary science , 32 : 363 – 401 .
   Web of Science ®Google Scholar
• Matthies , H.G. 1997 . Uncertainties in probabilistic numerical analysis of structures and solids–stochastic finite elements . Structural safety , 19 : 283 – 336 .
   Web of Science ®Google Scholar
• McKay , M. and Meyer , M. 2000 . Critique of and limitations on the use of expert judgements in accident consequence uncertainty analysis . Radiation protection dosimetry , 90 : 325 – 330 .
   Web of Science ®Google Scholar
• McKay , M.D. , Beckman , R.J. and Conover , W.J. 1979 . A comparison of three methods for selecting values of input variables in the analysis of output from a computer code . Technometrics , 21 : 239 – 245 .
   Web of Science ®Google Scholar
• Melchers , R.E. 1990 . Search-based importance sampling . Structural safety , 9 : 117 – 128 .
   Web of Science ®Google Scholar
• Meyer , M.A. and Booker , J.M. 1991 . Eliciting and analyzing expert judgment: a practical guide , New York : Academic Press .
   Google Scholar
• Moeller , D.W. and Ryan , M.T. 2005 . Sensitivity analyses of the standards for the proposed Yucca Mountain repository–a review, evaluation, and commentary . Health physics , 88 : 459 – 468 .
   PubMed Web of Science ®Google Scholar
• Mohanty , S. and Codell , R.B. 2004 . Independent Postclosure performance estimates of the proposed repository at Yucca Mountain . Nuclear technology , 148 : 105 – 114 .
   Web of Science ®Google Scholar
• Mohanty , S. and Sagar , B. 2002 . Importance of transparency and traceability in building a safety case for high-level nuclear waste repositories . Risk analysis , 22 : 7 – 15 .
   PubMed Web of Science ®Google Scholar
• Moore , R.E. 1966 . Interval analysis , Englewood Cliffs, NJ : Prentice Hall .
   Google Scholar
• Moore , R.E. 1979 . Methods and applications of interval analysis , Philadelphia, PA : Society for Industrial and Applied Mathematics .
   Google Scholar
• Neumaier , A. 1990 . Interval methods for systems of equations , Cambridge : Cambridge University Press .
   Google Scholar
• Nicola , V.F. , Shahabuddin , P. and Nakayama , M.K. 2001 . Techniques for fast simulation of models of highly dependable systems . IEEE transactions on reliability , 50 : 246 – 264 .
   Web of Science ®Google Scholar
• Nutt , W.T. and Wallis , G.B. 2004 . Evaluation of nuclear safety from the outputs of computer codes in the presence of uncertainties . Reliability engineering and system safety , 83 : 57 – 77 .
   Web of Science ®Google Scholar
• O'Hagan , A. 2006 . Bayesian analysis of computer code outputs: a tutorial . Reliability engineering and system safety , 91 : 1290 – 1300 .
   Web of Science ®Google Scholar
• Oberkampf , W.L. 2002 . Error and uncertainty in modeling and simulation . Reliability engineering and system safety , 75 : 333 – 357 .
   Web of Science ®Google Scholar
• Ortiz , N.R. 1991 . Use of expert judgment in NUREG-1150 . Nuclear engineering and design , 126 : 313 – 331 .
   Web of Science ®Google Scholar
• Owen , A. and Zhou , Y. 2000 . Safe and effective importance sampling . Journal of American statistical association , 95 : 135 – 143 .
   Web of Science ®Google Scholar
• Parry , G.W. and Winter , P.W. 1981 . Characterization and evaluation of uncertainty in probabilistic risk analysis . Nuclear safety , 22 : 28 – 42 .
   Google Scholar
• Paté-Cornell , M.E. 1996 . Uncertainties in risk analysis: six levels of treatment . Reliability engineering and system safety , 54 : 95 – 111 .
   Web of Science ®Google Scholar
• Patt , A. , Klein , R.J.T. and Vega-Leinert , A.D.L. 2005 . Taking the uncertainty in climate-change vulnerability assessment seriously . C.R. Geoscience , 337 : 411 – 424 .
   Web of Science ®Google Scholar
• Pollard , D. 2002 . A user's guide to measure theoretic probability , London, New York : Cambridge University Press .
   Google Scholar
• Reinert , J.M. and Apostolakis , G.E. 2006 . Including model uncertainty in risk-informed decision making . Annals of nuclear energy , 33 : 354 – 369 .
   Web of Science ®Google Scholar
• Ross , T.J. 2004 . Fuzzy logic with engineering applications , 2nd ed. , New York : Wiley .
   Google Scholar
• Ross , T.J. , Booker , J.M. and Parkinson , W.J. , eds. 2002 . Fuzzy logic and probability applications: bridging the gap , Philadelphia, PA : Society for Industrial and Applied Mathematics .
   Google Scholar
• Rowe , W.D. 1994 . Understanding uncertainty . Risk analysis , 14 : 743 – 750 .
   Web of Science ®Google Scholar
• Ruppert , D. , Ward , M.P. and Carroll , R.J. 2003 . Semiparametric regression , Cambridge : Cambridge University Press .
   Google Scholar
• Saltelli , A. and Tarantola , S. 2002 . On the relative importance of input factors in mathematical models: safety assessment for nuclear waste disposal . Journal of the American statistical association , 97 : 702 – 709 .
   Web of Science ®Google Scholar
• Saltelli , A. , Chan , K. and Scott , E.M. , eds. 2000 . Sensitivity analysis , New York : Wiley .
   Google Scholar
• Saltelli , A. 2005 . Sensitivity analysis for chemical models . Chemical reviews , 105 : 2811 – 2828 .
   PubMed Web of Science ®Google Scholar
• Shafer , G. 1976 . A mathematical theory of evidence , Princeton, NJ : Princeton University Press .
   Google Scholar
• Shahabuddin , P. 1994 . Importance sampling for the simulation of highly reliable markovian systems . Management science , 40 : 333 – 352 .
   Web of Science ®Google Scholar
• Sharp , D.H. and Wood-Schultz , M.M. 2003 . QMU and nuclear weapons certification: what's under the hood? . Los Alamos science , 28 : 47 – 53 .
   Google Scholar
• Simonoff , J.S. 1996 . Smoothing methods in statistics , New York : Springer-Verlag .
   Google Scholar
• Singh , V.P. , Strupczewski , W.G. and Weglarczyk , S. 2003 . “ Uncertainty in environmental analysis ” . In Integrated technologies for environmental monitoring and information production , Edited by: Harmancioglu , N.B. , Ozkul , S.D. , Fistikoglu , O. and Geerders , P. 141 – 158 . Boston, MA : Kluwer Academic Publishers .
   Google Scholar
• Smets , P. 1998 . “ Probability, possibility, belief: which and where? ” . In Handbook of defeasible reasoning and uncertainty management systems , Edited by: Grabbay , D.M. and Smets , P. 1 – 24 . Boston, MA : Kluwer Academic Publishers .
   Google Scholar
• Stepp , J.C. 2001 . Probabilistic seismic hazard analyses for ground motions and fault displacement at Yucca Mountain, Nevada . Earthquake spectra , 17 : 113 – 151 .
   Google Scholar
• Stigler , S.M. 1986 . The history of statistics: the measurement of uncertainty before 1900 , Cambridge, MA : Harvard University Press .
   Google Scholar
• Storlie , C.B. and Helton , J.C. 2008a . Multiple predictor smoothing methods for sensitivity analysis: description of techniques . Reliability engineering and system safety , 93 : 28 – 54 .
   Web of Science ®Google Scholar
• Storlie , C.B. and Helton , J.C. 2008b . Multiple predictor smoothing methods for sensitivity analysis: example results . Reliability engineering and system safety , 93 : 55 – 77 .
   Web of Science ®Google Scholar
• Thorne , M.C. and Williams , M.M.R. 1992 . A review of expert judgement techniques with reference to nuclear safety . Progress in nuclear safety , 27 : 83 – 254 .
   Google Scholar
• U.S. Department of Energy (U.S. DOE) . 1996 . Title 40 CFR Part 191 Compliance Certification Application for the Waste Isolation Pilot Plant , Vols. I-XXI , Carlsbad, NM : Department of Energy, Carlsbad Area Office, Waste Isolation Pilot Plant, DOE/CAO-1996-2184 .
   Google Scholar
• U.S. Nuclear Regulatory Commission (U.S. NRC) . 1990–1991 . Severe Accident Risks: an Assessment for Five U.S. Nuclear Power Plants , Vols. 1–3 , Washington, DC : U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research, Division of Systems Research, NUREG-1150 .
   Google Scholar
• Van Asselt , B.A. and Rotmans , J. 2002 . Uncertainty in integrated assessment modelling: from positivism to pluralism . Climatic change , 54 : 75 – 105 .
   Web of Science ®Google Scholar
• Vaughan , D.G. and Spouge , J.R. 2002 . Risk estimation of collapse of the West Antarctic ice sheet . Climatic change , 52 : 65 – 91 .
   Web of Science ®Google Scholar
• Wagner , R.L. 2003 . Science, uncertainty and risk: the problem of complex phenomena . APS news , 12 : 8
   Google Scholar
• Wasserman , L. 1988 . Belief functions and likelihood, technical report 420 , Pittsburgh, PA : Department of Statistics, Carnegie-Mellon University .
   Google Scholar
• Wasserman , L.A. 1990 . Belief functions and statistical inference . The Canadian journal of statistics , 18 : 183 – 196 .
   Web of Science ®Google Scholar
• Weatherford , R. 1982 . Philosophical foundations of probability theory , London, Boston : Routledge & Kegan Paul .
   Google Scholar
• Webster , M. and Cho , C.-H. 2006 . Analysis of variability and correlation in long-term economic growth rates . Energy economics , 28 : 653 – 666 .
   Web of Science ®Google Scholar
• Webster , M.D. 2002 . Uncertainty in emissions projections for climate models . Atmospheric environment , 36 : 3659 – 3670 .
   Web of Science ®Google Scholar
• Winkler , R.L. 1996 . Uncertainty in probabilistic risk assessment . Reliability engineering and system safety , 54 : 127 – 132 .
   Web of Science ®Google Scholar
• Wu , J.S. , Apostolakis , G.E. and Okrent , D. 1990 . Uncertainty in system analysis: probabilistic versus nonprobabilistic theories . Reliability engineering and system safety , 30 : 163 – 181 .
   Web of Science ®Google Scholar
• Zadeh , L.A. 1965 . Fuzzy sets . Information and control , 8 : 338 – 353 .
   Web of Science ®Google Scholar
• Zadeh , L.A. 1978 . Fuzzy sets as a basis for a theory of possibility . Fuzzy sets and systems , 1 : 3 – 28 .
   Google Scholar