Concerns, Challenges, and Directions of Development for the Issue of Representing Uncertainty in Risk Assessment

In the analysis of the risk associated to rare events that may lead to catastrophic consequences with large uncertainty, it is questionable that the knowledge and information available for the analysis can be reflected properly by probabilities. Approaches other than purely probabilistic have been suggested, for example, using interval probabilities, possibilistic measures, or qualitative methods. In this article, we look into the problem and identify a number of issues that are foundational for its treatment. The foundational issues addressed reflect on the position that “probability is perfect” and take into open consideration the need for an extended framework for risk assessment that reflects the separation that practically exists between analyst and decisionmaker.

[1]  Thierry Denoeux,et al.  Risk assessment based on weak information using belief functions: a case study in water treatment , 2006, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[2]  Alexander Karlsson Imprecise Probability , 2006 .

[3]  Rob P. Rechard,et al.  Historical background on performance assessment for the Waste Isolation Pilot Plant , 1999, Reliab. Eng. Syst. Saf..

[4]  J. Vrijling,et al.  An overview of quantitative risk measures for loss of life and economic damage. , 2003, Journal of hazardous materials.

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

[6]  Enrico Zio,et al.  Some considerations on the treatment of uncertainties in risk assessment for practical decision making , 2011, Reliab. Eng. Syst. Saf..

[7]  Terje Aven,et al.  Foundations of risk analysis : a knowledge and decision-oriented perspective , 2003 .

[8]  David I Blockley Fuzziness and probability: a discussion of Gaines5 axioms , 1985 .

[9]  Dennis V. Lindley,et al.  Understanding Uncertainty: Lindley/Understanding Uncertainty , 2006 .

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

[11]  Stephen D. Unwin,et al.  A Fuzzy Set Theoretic Foundation for Vagueness in Uncertainty Analysis , 1986 .

[12]  Terje Aven,et al.  Foundations of Risk Analysis: Aven/Foundations of Risk Analysis , 2012 .

[13]  D Warner North,et al.  Probability Theory and Consistent Reasoning , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[14]  J. Schreiber Foundations Of Statistics , 2016 .

[15]  H. D. De Kanter [The philosophy of statistics]. , 1972, Ginecología y Obstetricia de México.

[16]  T. Aven,et al.  Probability and Possibility‐Based Representations of Uncertainty in Fault Tree Analysis , 2013, Risk analysis : an official publication of the Society for Risk Analysis.

[17]  S. Kaplan,et al.  On The Quantitative Definition of Risk , 1981 .

[18]  E. Rosa Metatheoretical foundations for post-normal risk , 1998 .

[19]  Durga Rao Karanki,et al.  Uncertainty Analysis Based on Probability Bounds (P‐Box) Approach in Probabilistic Safety Assessment , 2009, Risk analysis : an official publication of the Society for Risk Analysis.

[20]  Stan Kaplan,et al.  The Words of Risk Analysis , 1997 .

[21]  Terje Aven,et al.  Interpretations of alternative uncertainty representations in a reliability and risk analysis context , 2011, Reliab. Eng. Syst. Saf..

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

[23]  James O. Berger,et al.  An overview of robust Bayesian analysis , 1994 .

[24]  Hung T. Nguyen,et al.  An Introduction to Random Sets , 2006 .

[25]  John Haigh,et al.  Probabilistic Risk Analysis: Foundations and Methods , 2003 .

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

[27]  David I Blockley,et al.  Analysing uncertainties: Towards comparing Bayesian and interval probabilities' , 2013 .

[28]  Scott Ferson,et al.  Arithmetic with uncertain numbers: rigorous and (often) best possible answers , 2004, Reliab. Eng. Syst. Saf..

[29]  David I Blockley,et al.  Measuring judgements to improve performance , 2005 .

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

[31]  Jon C. Helton,et al.  Quantification of margins and uncertainties: Conceptual and computational basis , 2011, Reliab. Eng. Syst. Saf..

[32]  E. Zio,et al.  A Combined Monte Carlo and Possibilistic Approach to Uncertainty Propagation in Event Tree Analysis , 2008, Risk analysis : an official publication of the Society for Risk Analysis.

[33]  Enrico Zio,et al.  Uncertainty in Risk Assessment: The Representation and Treatment of Uncertainties by Probabilistic and Non-Probabilistic Methods , 2013 .

[34]  L. Zadeh Probability measures of Fuzzy events , 1968 .

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

[36]  Didier Dubois,et al.  Unifying practical uncertainty representations - I: Generalized p-boxes , 2008, Int. J. Approx. Reason..

[37]  T. Aven,et al.  EXPRESSING AND COMMUNICATING UNCERTAINTY IN RELATION TO QUANTITATIVE RISK ANALYSIS , 2009 .

[38]  Frank P. A. Coolen,et al.  On the Use of Imprecise Probabilities in Reliability , 2004 .

[39]  Terje Aven,et al.  Practical implications of the new risk perspectives , 2013, Reliab. Eng. Syst. Saf..

[40]  Augustine Kong,et al.  Uncertain evidence and artificial analysis , 1990 .

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

[42]  Didier Dubois,et al.  Representation, Propagation, and Decision Issues in Risk Analysis Under Incomplete Probabilistic Information , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[43]  Roger M. Cooke,et al.  Deep and Shallow Uncertainty in Messaging Climate Change , 2014 .

[44]  Arie Tzvieli Possibility theory: An approach to computerized processing of uncertainty , 1990, J. Am. Soc. Inf. Sci..

[45]  Victoria Montgomery,et al.  New statistical methods in risk assessment by probability bounds , 2009 .

[46]  Pauline Coolen-Schrijner,et al.  Imprecision in Statistical Theory and Practice , 2009 .

[47]  T. Aven,et al.  On risk defined as an event where the outcome is uncertain , 2009 .

[48]  Terje Aven,et al.  On how to define, understand and describe risk , 2010, Reliab. Eng. Syst. Saf..

[49]  Philippe Smets,et al.  What is Dempster-Shafer's model? , 1994 .

[50]  E. Rosa The Social Amplification of Risk: The logical structure of the social amplification of risk framework (SARF): Meta theoretical foundations and policy implications , 2003 .

[51]  Enrico Zio,et al.  Uncertainty in Risk Assessment , 2014 .

[52]  Didier Dubois,et al.  Possibility theory and statistical reasoning , 2006, Comput. Stat. Data Anal..

[53]  D. G. Rees,et al.  Foundations of Statistics , 1989 .

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

[55]  R P Rechard,et al.  Historical Relationship Between Performance Assessment for Radioactive Waste Disposal and Other Types of Risk Assessment , 1999, Risk analysis : an official publication of the Society for Risk Analysis.

[56]  T Byrom,et al.  Doing it differently , 2014 .

[57]  L. Wasserman,et al.  Inferences from multinomial data: Learning about a bag of marbles - Discussion , 1996 .

[58]  Didier Dubois,et al.  Joint Propagation and Exploitation of Probabilistic and Possibilistic Information in Risk Assessment , 2006, IEEE Transactions on Fuzzy Systems.

[59]  Terje Aven,et al.  A semi-quantitative approach to risk analysis, as an alternative to QRAs , 2008, Reliab. Eng. Syst. Saf..

[60]  Frank P. A. Coolen,et al.  Imprecise reliability: An introductory overview , 2007, Intelligence in Reliability Engineering.

[61]  D. Richards,et al.  Understanding uncertainty , 2012, Evidence-Based Dentistry.

[62]  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.

[63]  J. Kacprzyk,et al.  Advances in the Dempster-Shafer theory of evidence , 1994 .

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

[65]  Vicki M. Bier,et al.  Uncertainty about probability: a reconciliation with the subjectivist viewpoint , 1996, IEEE Trans. Syst. Man Cybern. Part A.

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

[67]  David Banks Foundations of Risk Analysis: A Knowledge and Decision-Oriented Perspective , 2005 .

[68]  Nozer D. Singpurwalla,et al.  Reliability and risk , 2006 .

[69]  Kurt Weichselberger The theory of interval-probability as a unifying concept for uncertainty , 2000, Int. J. Approx. Reason..

[70]  Didier Dubois,et al.  Formal Representations of Uncertainty , 2010, Decision-making Process.

[71]  Ortwin Renn,et al.  Risk governance , 2011 .

[72]  Subir Ghosh,et al.  Reliability and Risk: A Bayesian Perspective , 2008, Technometrics.

[73]  Jon C. Helton,et al.  Alternative representations of epistemic uncertainty , 2004, Reliab. Eng. Syst. Saf..

[74]  Glenn Shafer,et al.  Perspectives on the theory and practice of belief functions , 1990, Int. J. Approx. Reason..

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

[76]  P. Walley Statistical Reasoning with Imprecise Probabilities , 1990 .

[77]  P. Walley Inferences from Multinomial Data: Learning About a Bag of Marbles , 1996 .