Assessing uncertainty in extreme events: Applications to risk-based decision making in interdependent infrastructure sectors

Abstract Risk-based decision making often relies upon expert probability assessments, particularly in the consequences of disruptive events and when such events are extreme or catastrophic in nature. Naturally, such expert-elicited probability distributions can be fraught with errors, as they describe events which occur very infrequently and for which only sparse data exist. This paper presents a quantitative framework, the extreme event uncertainty sensitivity impact method (EE-USIM), for measuring the sensitivity of extreme event consequences to uncertainties in the parameters of the underlying probability distribution. The EE-USIM is demonstrated with the Inoperability input–output model (IIM), a model with which to evaluate the propagation of inoperability throughout an interdependent set of economic and infrastructure sectors. The EE-USIM also makes use of a two-sided power distribution function generated by expert elicitation of extreme event consequences.

[1]  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.

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

[3]  S. Lichtenstein,et al.  Do those who know more also know more about how much they know?*1 , 1977 .

[4]  Wassily Leontief Input-Output Economics , 1966 .

[5]  Philippe Artzner Application of Coherent Risk Measures to Capital Requirements in Insurance , 1999 .

[6]  A. I. Shlyakhter,et al.  An improved framework for uncertainty analysis: Accounting for unsuspected errors , 1994 .

[7]  Yacov Y. Haimes,et al.  Risk modeling, assessment, and management , 1998 .

[8]  Kash Barker,et al.  Sequential Decision-making in Interdependent Sectors with Multiobjective Inoperability Decision Trees: Application to Biofuel Subsidy Analysis , 2008 .

[9]  David Vose,et al.  Monte Carlo Risk Analysis Modeling , 1996 .

[10]  Bilal M. Ayyub,et al.  Elicitation of expert opinions for uncertainty and risks: Answer to the Book Review by Roger M. Cooke , 2003, Fuzzy Sets Syst..

[11]  Ali Mosleh,et al.  The Assessment of Probability Distributions from Expert Opinions with an Application to Seismic Fragility Curves , 1986 .

[12]  Phhilippe Jorion Value at Risk: The New Benchmark for Managing Financial Risk , 2000 .

[13]  Samuel Kotz,et al.  A novel extension of the triangular distribution and its parameter estimation , 2002 .

[14]  Ted G. Eschenbach,et al.  Stochastic Sensitivity Analysis , 1990 .

[15]  W. Leontief,et al.  The structure of American economy, 1919-1929 : an empirical application of equilibrium analysis , 1942 .

[16]  Yacov Y. Haimes,et al.  System simulation for availability of weapon systems under various missions , 2005 .

[17]  Vicki M. Bier,et al.  A study of expert overconfidence , 2008, Reliab. Eng. Syst. Saf..

[18]  Yacov Y Haimes,et al.  Applying the Partitioned Multiobjective Risk Method (PMRM) to Portfolio Selection , 2004, Risk analysis : an official publication of the Society for Risk Analysis.

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

[20]  Samuel Kotz,et al.  Beyond Beta: Other Continuous Families Of Distributions With Bounded Support And Applications , 2004 .

[21]  Dirk Helbing,et al.  Modelling the Dynamics of Disaster Spreading in Networks , 2006 .

[22]  James H Lambert,et al.  A Risk‐Based Approach to Setting Priorities in Protecting Bridges Against Terrorist Attacks , 2004, Risk analysis : an official publication of the Society for Risk Analysis.

[23]  Yacov Y. Haimes,et al.  Sensitivity, responsivity, stability and irreversibility as multiple objectives in civil systems , 1977 .

[24]  M. Evans Statistical Distributions , 2000 .

[25]  Joost R. Santos,et al.  An integrated approach to customer elicitation for the aerospace sector , 2006 .

[26]  James H. Lambert,et al.  Risk of Extreme Events Under Nonstationary Conditions , 1998 .

[27]  Joost R. Santos,et al.  Modeling the Demand Reduction Input‐Output (I‐O) Inoperability Due to Terrorism of Interconnected Infrastructures * , 2004, Risk analysis : an official publication of the Society for Risk Analysis.

[28]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[29]  R. Hibbeler Engineering mechanics : statics and dynamics , 1989 .

[30]  Terry Williams,et al.  Practical Use of Distributions in Network Analysis , 1992 .

[31]  Y. Haimes,et al.  Risk Management for Leontief‐Based Interdependent Systems , 2004, Risk analysis : an official publication of the Society for Risk Analysis.

[32]  W. Leontief Quantitative Input and Output Relations in the Economic Systems of the United States , 1936 .

[33]  Samuel Kotz,et al.  Generalizations of Two-Sided Power Distributions and Their Convolution , 2003 .

[34]  James H. Lambert,et al.  Alternative measures of risk of extreme events in decision trees , 1999 .

[35]  Vlasta Molak,et al.  Fundamentals of Risk Analysis and Risk Management , 1996 .

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

[37]  N. Taleb Black Swans and the Domains of Statistics , 2007 .

[38]  James H. Lambert,et al.  Inoperability Input-Output Model for Interdependent Infrastructure Sectors. I: Theory and Methodology , 2005 .

[39]  Joost R. Santos,et al.  Extreme Risk Analysis of Interdependent Economic and Infrastructure Sectors , 2007, Risk analysis : an official publication of the Society for Risk Analysis.

[40]  Vicki M. Bier,et al.  Implications of the research on expert overconfidence and dependence , 2004, Reliab. Eng. Syst. Saf..

[41]  David Johnson,et al.  The triangular distribution as a proxy for the beta distribution in risk analysis , 1997 .

[42]  Joost R. Santos Interdependency analysis with multiple probabilistic sector inputs , 2008 .

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

[44]  David E. Burmaster,et al.  Assessment of Variability and Uncertainty Distributions for Practical Risk Analyses , 1994 .

[45]  Robert Dorfman,et al.  WASSILY LEONTIEF'S CONTRIBUTION TO ECONOMICS , 1973 .

[46]  Michael L. Lahr,et al.  Input-output analysis: frontiers and extensions , 2001 .

[47]  Jon C. Helton,et al.  Challenge Problems : Uncertainty in System Response Given Uncertain Parameters ( DRAFT : November 29 , 2001 ) , 2001 .

[48]  Igor Rychlik,et al.  Probability and Risk Analysis: An Introduction for Engineers , 2006 .

[49]  Yacov Y. Haimes,et al.  A Risk-based Input–Output Methodology for Measuring the Effects of the August 2003 Northeast Blackout , 2007 .

[50]  Dirk Helbing,et al.  Efficient response to cascading disaster spreading. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[51]  James H. Lambert,et al.  Inoperability Input-Output Model for Interdependent Infrastructure Sectors. II: Case Studies , 2005 .

[52]  E. Andrijcic,et al.  A Macro‐Economic Framework for Evaluation of Cyber Security Risks Related to Protection of Intellectual Property , 2006, Risk analysis : an official publication of the Society for Risk Analysis.

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

[54]  Hendrik I. Frohwein,et al.  Risk of Extreme Events in Multiobjective Decision Trees Part 1. Severe Events , 2000, Risk analysis : an official publication of the Society for Risk Analysis.

[55]  James A. Constantine,et al.  SysML modeling of off-the-shelf-option acquisition for risk mitigation in military programs , 2010 .

[56]  Norman J. McCormick,et al.  Reliability and Risk Analysis , 1981, IEEE Transactions on Reliability.

[57]  S. Kotz,et al.  The Standard Two-Sided Power Distribution and its Properties , 2002 .

[58]  Yacov Y Haimes,et al.  Systemic Valuation of Strategic Preparedness Through Application of the Inoperability Input‐Output Model with Lessons Learned from Hurricane Katrina , 2007, Risk analysis : an official publication of the Society for Risk Analysis.

[59]  A. Rose Economic Principles, Issues, and Research Priorities in Hazard Loss Estimation , 2004 .

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

[61]  Y. Haimes,et al.  Leontief-Based Model of Risk in Complex Interconnected Infrastructures , 2001 .

[62]  Walter E. Beyeler,et al.  Assessing infrastructure interdependencies: the challenge of risk analysis for complex adaptive systems , 2004, Int. J. Crit. Infrastructures.

[63]  Anita Raja,et al.  Critical Infrastructure Integration Modeling and Simulation , 2004, ISI.

[64]  Yacov Y. Haimes,et al.  The uncertainty sensitivity index method (USIM) and its extension , 1988 .

[65]  Yacov Y. Haimes,et al.  Journal of Homeland Security and Emergency Management A Roadmap for Quantifying the Efficacy of Risk Management of Information Security and Interdependent , 2011 .