The Epistemic Uncertainty Project, through the sponsorship of Sandia National Laboratories, recently held the "Epistemic Uncertainty Workshop." The Workshop was held August 6-7, 2002, at the Marriott Hotel in Albuquerque, New Mexico. The purpose of the Workshop was to bring together traditional probabilists, Bayesians, generalized information theorists, and decision theorists. These researchers were joined by leading reliability engineering and risk analysts who face the issue of epistemic and aleatory uncertainty in the assessment of high consequence engineered and natural systems.

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To focus attention and discussion on the topic of epistemic uncertainty, the organizing committee constructed a sequence of challenge problems. All of the invited papers and submitted papers were requested to solve at least some of these problems. Each of the challenge problems dealt with the representation and aggregation of mixtures of epistemic and aleatory uncertainty and the propagation of these mixtures through a simple mathematical model. The first model was given by an algebraic equation and the second model was given by a linear ordinary differential equation. The problems were intended to serve as a common focus and challenge for experimentation, discussion, and comparison of multiple approaches to the problems. We were interested in the problem sets only to the extent they are surrogates for real problems. Each author chose which of these problems they addressed in their paper. More detail concerning the problem sets and their context in engineering and risk analysis is given in (www.sandia.gov/epistemic/challenge.htm) “Challenge Problems: Uncertainty in System Response Given Uncertain Parameters”.

There were 14 invited papers presented by internationally known researchers in the field. Seven submitted papers were selected from extended abstracts submitted. At the author’s discretion, the final version of paper presented at the Workshop will be reviewed for publication in a special issue of the journal Reliability Engineering and System Safety. The Guest Editor for the special issue will be Jon Helton, a member of the organizing committee. For consideration in the special issue, the final version of the paper will be due no later than October 1, 2002.

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Paper Publication Status

There have been a total of 22 papers submitted for review for the special issue of the journal Reliability Engineering and System Safety. A summary of the status of the paper, as of Feb. 19, 2003, is: 8 have been completed for publication, 7 are in revision, 4 are in review, and 3 are in the final stages of completion. A listing of all of the papers and their status is:

H. Agarwal, J.E. Renaud, E.L. Preston and D. Padmanabhan (University of Notre Dame), "Uncertainty Quantification Using Evidence Theory in Multidisciplinary Design Optimization" (complete)

B. M. Ayyub (University of Maryland), "From Dissecting Ignorance to Solving Algebraic Problems" (complete)

Y. Ben-Haim (Tecnhnion, Israel), "Uncertainty, Probability and Information-gaps" (in review)

D. Berleant and J. Zhang (Iowa State University) "Representation and Problem Solving with the Distribution Envelope Determination (DEnv) Method" (in revision)

V. Bier (University of Wisconsin-Madison), "Implications of the Research on Expert Overconfidence and Dependence" (in revision)

J. M. Booker and L. A. McNamara (Los Alamos National Laboratory), "Solving the Challenge Problems Using Expert Knowledge Theory and Methods" (in revision)

R. M. Cooke (Delft University of Technology, Netherlands), "The Anatomy of the Squizzel: The Role of Operational Definitions in Representing Uncertainty" (in revision)

G. de Cooman and M. C. M. Troffaes (Universiteit Gent, Belgium), "Solving the First Sandia Problem Set Using the Theory of Coherent Lower Previsions" (in review)

S.A. Ferson and J. Hajagos (Applied Biomathematics and State University of New York at Stony Brook), "Rigorous and (Often) Best-possible Answers to All the Challenge Problems" (in revision)

T. Fetz and M. Oberguggenberger (University of Innsbruck, Austria), "Propagation of Uncertainty through Multivariate Functions in the Framework of Sets of Probability Measures" (complete)

J. Hall and J. Lawry (University of Bristol, United Kingdom), "Generation, Combination and Extension of Random Set Approximations to Coherent Lower and Upper Probabilities" (complete)

J. C. Helton, J. D. Johnson, and W. L. Oberkampf (Sandia National Laboratories), "An Exploration of Alternative Approaches to the Representation of Uncertainty in Model Predictions" (in preparation)

M. Hyman and Weiye Li (Los Alamos National Laboratory), "Data Structures and Computer Arithmetic for Quantifying Uncertainty" (in preparation)

G. Klir (Binghamton University, Binghamton, New York), "Generalized Uncertainty-Based Information Theory: Aims, Results, and Open Problems" (complete)

V. Kreinovich (University of Texas at El Paso) and S.A. Ferson(Applied Biomathematics), "A New Cauchy-based Black-box Technique for Uncerainty in Risk Analysis" (complete)

I. Kozine (RISO National Laboratory, Denmark) and L. Utkin (Munich University, Germany), "An Approach to Combining Unreliable Pieces of Evidence and Their Propagation in a System Response Analysis" (in review)

A. O'Hagan and J.E. Oakley (University of Sheffield, United Kingdom), "Probability Is Perfect, but We Can't Elicit It Perfectly" (in revision)

J. R. Red-Horse and A. S. Benjamin (Sandia National Laboratories), "A Probabilistic Approach to Uncertainty Quantification with Limited Information" (in revision)

B. Rutherford (Sandia National Laboratories), "A Response Modeling Approach to Charaterization and Propagation of Uncerainty Specified over Intervals" (in review)

P. Soundappan(University of Florida, Gainesville), E. Nikolaidis (University of Toledo, Ohio), R. T. Haftka (Wright State University, Dayton, Ohio), R. Grandhi(Wright State University), and R. Canfield (Air Force Institute of Technology, Dayton, Ohio), "Comparison of Evidence Theory and Bayesian Theory for Uncertainty Modeling" (complete)

F. Tonon (University of Utah), "Using Random Set Theory to Propagate Uncertainty through a Mechanical System" (complete)

R. R. Yager (Iona College, New Rochelle) "Uncertainty Modeling and Decision Support" (in preparation)

After the completion of the Workshop, many participants commented about how pleased they were with the presentations and the lengthy discussions. Many felt it was one of their best experiences at a conference or workshop because of the depth of the conversations and debates, both during the presentations and after the formal sessions.

The organizing committee sincerely thanks all of the attendees at the Workshop for their participation and energy. The Workshop has contributed to a better understanding of the diverse viewpoints toward representation and interpretation of epistemic uncertainty.

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