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

[1]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[2]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[3]  A. Dempster.  Upper and lower probability inferences based on a sample from a finite univariate population. , 1967, Biometrika.

[4]  H. Seal.  Studies in the history of probability and statistics , 1977 .

[5]  T. Fine.  Theories of Probability: An Examination of Foundations , 1973 .

[6]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[7]  W. Cleveland.  Robust Locally Weighted Regression and Smoothing Scatterplots , 1979 .

[8]  R. Iman,et al.  The Use of the Rank Transform in Regression , 1979 .

[9]  J. Friedman,et al.  Projection Pursuit Regression , 1981 .

[10]  G. W. Parry,et al.  Characterization and evaluation of uncertainty in probabilistic risk analysis , 1981 .

[11]  James E. Campbell,et al.  An Approach to Sensitivity Analysis of Computer Models: Part I—Introduction, Input Variable Selection and Preliminary Variable Assessment , 1981 .

[12]  R. Iman,et al.  A distribution-free approach to inducing rank correlation among input variables , 1982 .

[13]  R. Iman,et al.  Rank correlation plots for use with correlated input variables , 1982 .

[14]  David Lindley.  Scoring rules and the inevitability of probability , 1982 .

[15]  Leo Breiman,et al.  Classification and Regression Trees , 1984 .

[16]  R. Lowen,et al.  On the fundamentals of fuzzy sets. , 1984 .

[17]  David Lindley,et al.  The Probability Approach to the Treatment of Uncertainty in Artificial Intelligence and Expert Systems , 1987 .

[18]  Peter C. Cheeseman,et al.  An inquiry into computer understanding , 1988, Comput. Intell..

[19]  S. Stigler,et al.  The History of Statistics: The Measurement of Uncertainty before 1900 by Stephen M. Stigler (review) , 1986, Technology and Culture.

[20]  G. Klir.  IS THERE MORE TO UNCERTAINTY THAN SOME PROBABILITY THEORISTS MIGHT HAVE US BELIEVE , 1989 .

[21]  D. Dubois,et al.  Fuzzy sets, probability and measurement , 1989 .

[22]  Donald L. Iglehart,et al.  Importance sampling for stochastic simulations , 1989 .

[23]  Ronald L. Iman,et al.  Expert opinion in risk analysis: the NUREG-1150 methodology , 1989 .

[24]  C. T. Haan.  Parametric Uncertainty in Hydrologic Modeling , 1989 .

[25]  G. Apostolakis,et al.  Uncertainties in system analysis: Probabilistic versus nonprobabilistic theories , 1990 .

[26]  B. Kosko.  Fuzziness vs. probability , 1990 .

[27]  A. Saltelli,et al.  Non-parametric statistics in sensitivity analysis for model output: A comparison of selected techniques , 1990 .

[28]  G. Apostolakis.  The concept of probability in safety assessments of technological systems. , 1990, Science.

[29]  Ronald Fagin,et al.  Two Views of Belief: Belief as Generalized Probability and Belief as Evidence , 1992, Artif. Intell..

[30]  R. Melchers.  Search-based importance sampling , 1990 .

[31]  L. Wasserman.  Belief functions and statistical inference , 1990 .

[32]  R. Tibshirani,et al.  Generalized Additive Models , 1991 .

[33]  J. Friedman.  Multivariate adaptive regression splines , 1990 .

[34]  G. Klir,et al.  Generalized information theory , 1991 .

[35]  Ronald L. Iman,et al.  The Repeatability of Uncertainty and Sensitivity Analyses for Complex Probabilistic Risk Assessments , 1991 .

[36]  Ralph L. Keeney,et al.  Eliciting probabilities from experts in complex technical problems , 1991 .

[37]  R. Cooke.  Experts in Uncertainty: Opinion and Subjective Probability in Science , 1991 .

[38]  W. B. Murfin,et al.  The NUREG-1150 probabilistic risk assessment for the Sequoyah Nuclear Plant☆ , 1992 .

[39]  Jon C. Helton,et al.  Summary description of the methods used in the probabilistic risk assessments for NUREG-1150 , 1992 .

[40]  A. C. Payne,et al.  The NUREG-1150 probabilistic risk assessment for the Peach Bottom Atomic Power Station , 1992 .

[41]  W. B. Murfin,et al.  The NUREG-1150 probabilistic risk assessment for the Surry Nuclear Power Station☆ , 1992 .

[42]  W. Härdle.  Applied Nonparametric Regression , 1992 .

[43]  T. D. Brown,et al.  The NUREG-1150 probabilistic risk assessment for the Grand Gulf Nuclear Station , 1992 .

[44]  Philip Heidelberger,et al.  A Unified Framework for Simulating Markovian Models of Highly Dependable Systems , 1992, IEEE Trans. Computers.

[45]  F. W. Whicker,et al.  Contaminant Transport through Agroecosystems: Assessing Relative Importance of Environmental, Physiological, and Management Factors. , 1992, Ecological applications : a publication of the Ecological Society of America.

[46]  Ulrich W. Kulisch,et al.  Numerical Toolbox for Verified Computing I , 1993 .

[47]  E Ackerman,et al.  Parameter sensitivity of a model of viral epidemics simulated with Monte Carlo techniques. IV. Parametric ranges and optimization. , 1993, International journal of bio-medical computing.

[48]  Wallace B. Whiting,et al.  Effect of uncertainties in thermodynamic data and model parameters on calculated process performance , 1993 .

[49]  Hadi Dowlatabadi,et al.  Sensitivity and Uncertainty Analysis of Complex Models of Disease Transmission: an HIV Model, as an Example , 1994 .

[50]  Perwez Shahabuddin,et al.  Importance sampling for the simulation of highly reliable Markovian systems , 1994 .

[51]  F. O. Hoffman,et al.  Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. , 1994, Risk analysis : an official publication of the Society for Risk Analysis.

[52]  Jon C. Helton,et al.  Treatment of Uncertainty in Performance Assessments for Complex Systems , 1994 .

[53]  D. Hamby.  A review of techniques for parameter sensitivity analysis of environmental models , 1994, Environmental monitoring and assessment.

[54]  Jon C. Helton,et al.  Robustness of an uncertainty and sensitivity analysis of early exposure results with the MACCS reactor accident consequence model , 1995 .

[55]  Philip Heidelberger,et al.  Fast simulation of rare events in queueing and reliability models , 1993, TOMC.

[56]  Da Ruan,et al.  Foundations and Applications of Possibility Theory , 1995 .

[57]  W. Woodall,et al.  A probabilistic and statistical view of fuzzy methods , 1995 .

[58]  Nikolay Ivanov Kolev,et al.  Uncertainty and sensitivity analysis of a postexperiment simulation of nonexplosive melt-water interaction , 1996 .

[59]  Jon C. Helton,et al.  Guest editorial: treatment of aleatory and epistemic uncertainty in performance assessments for complex systems , 1996 .

[60]  M S Chan,et al.  The consequences of uncertainty for the prediction of the effects of schistosomiasis control programmes , 1996, Epidemiology and Infection.

[61]  M. Elisabeth Paté-Cornell,et al.  Uncertainties in risk analysis: Six levels of treatment , 1996 .

[62]  M. G. Marietta,et al.  Uncertainty and sensitivity analysis results obtained in the 1992 performance assessment for the waste isolation pilot plant , 1996 .

[63]  Laura Toran,et al.  Subsurface stormflow modeling with sensitivity analysis using a Latin-hypercube sampling technique , 1996 .

[64]  S. Ferson,et al.  Different methods are needed to propagate ignorance and variability , 1996 .

[65]  Robert L. Winkler,et al.  Uncertainty in probabilistic risk assessment , 1996 .

[66]  J. C. Helton,et al.  Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty , 1997 .

[67]  S. Blower,et al.  Uncertainty and sensitivity analysis of the basic reproductive rate. Tuberculosis as an example. , 1997, American journal of epidemiology.

[68]  Dov M. Gabbay,et al.  Handbook of defeasible reasoning and uncertainty management systems: volume 2: reasoning with actual and potential contradictions , 1998 .

[69]  Alex H. Barbat,et al.  Monte Carlo techniques in computational stochastic mechanics , 1998 .

[70]  Philippe Smets,et al.  Probability, Possibility, Belief: Which and Where? , 1998 .

[71]  William Greenwood,et al.  The history of nuclear weapon safety devices , 1998 .

[72]  Hal Caswell,et al.  HARBOR PORPOISE AND FISHERIES: AN UNCERTAINTY ANALYSIS OF INCIDENTAL MORTALITY , 1998 .

[73]  Didier Dubois,et al.  Possibility Theory: Qualitative and Quantitative Aspects , 1998 .

[74]  J. Simonoff.  Smoothing Methods in Statistics , 1998 .

[75]  C. Allin Cornell,et al.  Use of Technical Expert Panels: Applications to Probabilistic Seismic Hazard Analysis * , 1998 .

[76]  L. Yang.  Fuzzy Logic with Engineering Applications , 1999 .

[77]  D. Harmanec.  MEASURES OF UNCERTAINTY AND INFORMATION , 1999 .

[78]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[79]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[80]  Eduard Hofer,et al.  Sensitivity analysis in the context of uncertainty analysis for computationally intensive models , 1999 .

[81]  M. D. McKay,et al.  A comparison of three methods for selecting values of input variables in the analysis of output from a computer code , 2000 .

[82]  D. Dubois,et al.  Fundamentals of fuzzy sets , 2000 .

[83]  Hung T. Nguyen,et al.  Possibility Theory, Probability and Fuzzy Sets Misunderstandings, Bridges and Gaps , 2000 .

[84]  H. Gershengorn,et al.  A tale of two futures: HIV and antiretroviral therapy in San Francisco. , 2000, Science.

[85]  D. Pontier,et al.  A discrete-event computer model of feline herpes virus within cat populations. , 2000, Preventive Veterinary Medicine.

[86]  Richard J. Beckman,et al.  A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output From a Computer Code , 2000, Technometrics.

[87]  M. Mckay,et al.  Critique of and Limitations on the Use of Expert Judgements in Accident Consequence Uncertainty Analysis , 2000 .

[88]  Tim B. Swartz,et al.  Approximating Integrals Via Monte Carlo and Deterministic Methods , 2000 .

[89]  A. Owen,et al.  Safe and Effective Importance Sampling , 2000 .

[90]  Marvin K. Nakayama,et al.  Techniques for fast simulation of models of highly dependable systems , 2001, IEEE Trans. Reliab..

[91]  Kathleen V. Diegert,et al.  Error and uncertainty in modeling and simulation , 2002, Reliab. Eng. Syst. Saf..

[92]  H Christopher Frey,et al.  OF SENSITIVITY ANALYSIS , 2001 .

[93]  J. C. Helton,et al.  Bounds on belief and plausibility of functionally propagated random sets , 2002, 2002 Annual Meeting of the North American Fuzzy Information Processing Society Proceedings. NAFIPS-FLINT 2002 (Cat. No. 02TH8622).

[94]  F. J. Davis,et al.  Illustration of Sampling‐Based Methods for Uncertainty and Sensitivity Analysis , 2002, Risk analysis : an official publication of the Society for Risk Analysis.

[95]  Jon C. Helton,et al.  Latin Hypercube Sampling and the Propagation of Uncertainty in Analyses of Complex Systems , 2002 .

[96]  J. Charles Kerkering,et al.  Eliciting and Analyzing Expert Judgment, A Practical Guide , 2002, Technometrics.

[97]  Jane M. Booker,et al.  Fuzzy Logic and Probability Applications , 2002, Fuzzy Logic and Probability Applications.

[98]  F. J. Davis,et al.  Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems , 2002, Reliab. Eng. Syst. Saf..

[99]  R. Cooke.  Elicitation of expert opinions for uncertainty and risks , 2003 .

[100]  W. T. Tucker,et al.  Dependence in probabilistic modeling, Dempster-Shafer theory, and probability bounds analysis. , 2004 .

[101]  Roger M. Cooke,et al.  The anatomy of the squizzel: The role of operational definitions in representing uncertainty , 2004, Reliab. Eng. Syst. Saf..

[102]  D. Cacuci,et al.  A Comparative Review of Sensitivity and Uncertainty Analysis of Large-Scale Systems—II: Statistical Methods , 2004 .

[103]  王东东,et al.  Computer Methods in Applied Mechanics and Engineering , 2004 .

[104]  Joseph A. C. Delaney.  Sensitivity analysis , 2018, The African Continental Free Trade Area: Economic and Distributional Effects.

[105]  George J. Klir,et al.  Generalized information theory: aims, results, and open problems , 2004, Reliab. Eng. Syst. Saf..

[106]  Efstratios Nikolaidis,et al.  Engineering Design Reliability Handbook , 2004 .

[107]  Jeremy E. Oakley,et al.  Probability is perfect, but we can't elicit it perfectly , 2004, Reliab. Eng. Syst. Saf..

[108]  J. Tinsley Oden,et al.  Verification and validation in computational engineering and science: basic concepts , 2004 .

[109]  R. Cooke,et al.  Expert judgement elicitation for risk assessments of critical infrastructures , 2004 .

[110]  B. Ripley,et al.  Semiparametric Regression: Preface , 2003 .

[111]  Jon C. Helton,et al.  An exploration of alternative approaches to the representation of uncertainty in model predictions , 2003, Reliab. Eng. Syst. Saf..

[112]  Marion Kee,et al.  Analysis , 2004, Machine Translation.

[113]  Jay D. Johnson,et al.  Competing Failure Risk Analysis Using Evidence Theory , 2005, Risk analysis : an official publication of the Society for Risk Analysis.

[114]  Jon C. Helton,et al.  Multiple predictor smoothing methods for sensitivity analysis , 2005, Proceedings of the Winter Simulation Conference, 2005..

[115]  Jon C. Helton,et al.  A comparison of uncertainty and sensitivity analysis results obtained with random and Latin hypercube sampling , 2005, Reliab. Eng. Syst. Saf..

[116]  G. Klir.  Uncertainty and Information: Foundations of Generalized Information Theory , 2005 .

[117]  A. O'Hagan,et al.  Statistical Methods for Eliciting Probability Distributions , 2005 .

[118]  Vladik Kreinovich,et al.  Convergence properties of an interval probabilistic approach to system reliability estimation , 2005, Int. J. Gen. Syst..

[119]  Michael Andrew Christie,et al.  Error analysis and simulations of complex phenomena , 2005 .

[120]  Sandia Report,et al.  Survey of Sampling-Based Methods for Uncertainty and Sensitivity Analysis , 2006 .

[121]  G. Klir.  Measure of Uncertainty and Information , 2006 .

[122]  Alex M. Andrew,et al.  Uncertainty and Information: Foundations of Generalized Information Theory , 2006 .

[123]  Jon C. Helton,et al.  Survey of sampling-based methods for uncertainty and sensitivity analysis , 2006, Reliab. Eng. Syst. Saf..

[124]  Jon C. Helton,et al.  Sensitivity analysis in conjunction with evidence theory representations of epistemic uncertainty , 2006, Reliab. Eng. Syst. Saf..

[125]  Jon C. Helton,et al.  Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links , 2006, Reliab. Eng. Syst. Saf..

[126]  Jon C. Helton,et al.  Multiple predictor smoothing methods for sensitivity analysis: Example results , 2008, Reliab. Eng. Syst. Saf..

[127]  Arthur P. Dempster,et al.  A Generalization of Bayesian Inference , 1968, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[128]  Jon C. Helton,et al.  Multiple predictor smoothing methods for sensitivity analysis: Description of techniques , 2008, Reliab. Eng. Syst. Saf..

[129]  K. Fernow.  New York , 1896, American Potato Journal.

[130]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[131]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[132]  Didier Dubois,et al.  Possibility theory , 2018, Scholarpedia.

[133]  D. Sharp,et al.  QMU and Nuclear Weapons Certification What ’ s under the hood ? , 2022 .