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  • Print publication year: 2003
  • Online publication date: June 2012

6 - Uncertain Risk: The Role and Limits of Quantitative Assessment



The assessment and management of uncertain risks is an essential component of science, engineering, medicine, business, law, and other modern disciplines. I. Good argues that risk science based on the evaluation of probabilistic events has been useful in saving and improving lives throughout history, “since the assessment of uncertainty incorporates the idea of learning from experience which most creatures do” (Good, 1959). Learning from experience is only part of the challenge, since many decisions involve new or evolving risk scenarios in which humans have little or no experience. Risk management capabilities must include the ability to respond to risks that are known and well understood, and the ability to detect and anticipate those that are newly emerging (e.g., U.S. EPA SAB, 1995; NRC, 1999; U.S. EPA ORD, 2000). Uncertainty analysis provides a framework for characterizing the position of a problem along this continuum and the implications for appropriate response and management.

Uncertainty about risk arises as a result of a fundamental lack of understanding about how the world works, randomness in the outcome of natural and human processes, and an inability to measure, characterize, or even at times define key quantities of interest that affect, or are affected by, risk. Risks can vary across time, space, and from individual to individual in a population. Characterization of these variations is an essential part of a risk analysis; however, the basic knowledge or data to fully and effectively characterize risk, and its variability, are often lacking.

Adlassnig, K.-P. 1986. Fuzzy set theory in medical diagnosis. IEEE Transactions on Systems, Man and Cybernetics, SMC-16: 260–5
Andrews, R. 1997. Risk-based decision making. In Environmental Policy in the 1990s, N. Vig and M. Kraft, eds., Congressional Quarterly, 208–230, Washington, DC
Apostolakis, G. E. and Pickett, S. E.. 1998. Deliberation: Integrating analytical results into environmental decision involving multiple stakeholders. Risk Analysis, 18 (5): 621–47
Ashby, D., and Hutton, J. L. 1996. Bayesian epidemiology. In D. K. Berry, ed., Bayesian Biostatistics, pp. 109–38. Marcel Dekker, New York
Bankes, S. C. 1993. Exploratory modeling for policy analysis. Operations Research, 41: 435–49
Bankes, S. C. 1994. Computational experiments and exploratory modeling. Chance, 7 (1): 50–1, 57
Bedford, T., and R. Cooke. 2001. Probabilistic Risk Analysis: Foundations and Methods, Cambridge University Press, Cambridge
Berry, D. A. and Stangl, D. K., eds. 1996. Bayesian Biostatistics. Marcel Dekker, New York
Bier, V. M., Haimes, Y. Y., Lambert, J. H., Ferson, S., and Small, M. J. 2003. Quantifying risk of extreme or rare events: Lessons from a selection of approaches. This volume.
Bier, V. M., Haimes, Y. Y., Lambert, J. H., Matalas, N. C., and Zimmerman, R. 1999. A survey of approaches for assessing and managing the risk of extremes. Risk Analysis, 19 (1): 83–94
Bogen, K. T. 1990. Uncertainty in Environmental Health Risk Assessment, Garland Publishing, New York
Bogen, K. T. 1995. Methods to approximate joint uncertainty and variability in risk. Risk Analysis, 15 (3): 411–19
Bostrom, A., Fischhoff, B., and Morgan, M. G. 1992. Characterizing mental models of hazardous processes: A methodology with an application to radon. J. Social Issues, 48 (4): 85–100
Boudet, C., Zmirou, D., Laffond, M., Balducci, F., and Benoit-Guyod, J-L. 1999. Health risk assessment of a modern municipal waste incinerator. Risk Analysis, 19: 1215–22
Brasquet, C., Bourges, B., and Cloirec, P. 1999. Quantitative structure-property relationship (QSPR) for the adsorption of organic compounds onto activated carbon cloth: Comparison between multiple linear regression and neural network. Environmental Science and Technology, 33 (23): 4226–31
Brattin, W. J., Barry, T. M., and Chiu, N. 1996. Monte Carlo modeling with uncertain probability density functions. Human and Ecological Risk Assessment, 2 (4): 820–40
Brieman, L., Friedman, J. H., Olshen, R. A., and Stone, C. J. 1984. Classification and regression trees. Wadsworth&Brooks/Cole Advanced Books & Software, Pacific Grove, CA
Browner, C. 1995. Policy for Risk Characterization at the US Environmental Protection Agency, Memorandum to assistant and regional administrators
Bumb, R. R., Crummet, W. B., Cutie, S. S., Gledhill, J. R., Hummel, R. H., Kagel, R. O., Lamparski, L. L., Luoma, E. V., Miller, D. L., Nestrick, T. J., Shadoff, L. A., Stehl, R. H., and Woods, J. S. 1980. Trace chemistries of fire: A source of chlorinated dioxins. Science 210 (4468): 385–90
Burmaster, D. E., and Thompson, K. M. 1997. Estimating exposure point concentrations for surface soils for use in deterministic and probabilistic risk assessments. Human and Ecological Risk Assessment, 3 (3): 363–84
Burmaster, D. E., and Thompson, K. M. 1998. Fitting second-order parametric distributions to data using maximum likelihood estimation. Human and Ecological Risk Assessment, 4 (2): 319–39
Burmaster, D. E., and Wilson, A. M. 1996. An introduction to second-order random variables in human health risk assessment. Human and Ecological Risk Assessment, 2 (4): 892–919
Cao, H., and Chen, G. 1983. Some applications of fuzzy sets to meteorological forecasting. Fuzzy Sets and Systems, 9: 1–12
Carrington, C. D. 1996. Logical probability and risk assessment. Human and Ecological Risk Assessment, 2: 62
Carrington, C. D. 1997. An administrative view of model uncertainty in public health. Risk, 8: 273ff. See also:
Cash, D. W. 2000. Distributed assessment systems: An emerging paradigm of research, assessment, and decision-making for environmental change. Global Environmental Change, 10 (4): 241–4
Casman, E. A., Morgan, M. G., and Dowlatabadi, H. 1999. Mixed levels of uncertainty in complex policy models. Risk Analysis, 19 (1): 33–42
Chaloner, K. 1996. Elicitation of prior distributions. In D. K. Berry Stangl, ed., Bayesian Biostatistics, pp. 141–56. Marcel Dekker, New York
Charniak, E. 1991. Bayesian networks without tears. AI Magazine, 12 (4): 50–63
Clark, W. C., and Dickson, N. M. 1999. The global environmental assessment project: Learning from efforts to link science and policy in an interdependent world. Acclimations, 8: 6–7.
Clarke, L. 1988. Politics and bias in risk assessment. The Social Science Journal, 15: 155–65
Cooke, R. M. 1991. Experts in Uncertainty: Opinion and Subjective Probability in Science. Oxford Press, New York
Costello, C. J., Adams, R. M., and Polasky, S. (1998). The value of El Niño forecasts in the management of salmon: A stochastic dynamic assessment. American Journal of Agricultural Economics, 80: 765–77
Covello, V. T., and Mumpower, J. 1985. Risk analysis and risk management: A historical perspective. Risk Analysis, 5: 103–20
Cox, D. C., and Baybutt, P. 1981. Methods for uncertainty analysis: A comparative study. Risk Analysis, 1: 251–8
CRAM Presidential/Congressional Commission on Risk Assessment and Risk Management. 1997. Risk Assessment and Risk Management in Regulatory Decision Making. Final Report. Washington, DC
Cullen, A. C. 1994. Measures of conservatism in probabilistic risk assessment. Risk Analysis, 14: 389–93
Cullen, A. C. 1995. The sensitivity of Monte Carlo simulation results to model assumptions: The case of municipal solid waste combustor risk assessment. Journal of Air Waste Management Association, 45: 538–46
Cullen, A. C., and Eschenroeder, A. Q. 1997. Coping with muncipal waste. In J. Graham and J. Hartwell eds., The Greening of Industry. Harvard University Press, Cambridge, MA
Cullen, A. C., and Frey, H. C. 1999. Probabilistic Techniques in Exposure Assessment: A Handbook for Dealing with Variability and Uncertainty in Models and Inputs. Plenum Press, New York
Dakins, M. E., Toll, J. E., Small, M. J., and Brand, K. P. 1996. Risk-based environmental remediation: Bayesian Monte Carlo analysis and the expected value of sample information. Risk Analysis, 16 (1): 67–79
De Finetti, B. 1937. La Prevision: Ses Lois Logiques, Ses Sources Subjectives. Annales de L'Institut Henri Poincaré, 7 (1). pp. 1–68. English translation in H. Kyburg and H. Smokler, eds. 1964. Studies in Subjective Probability. Wiley, New York
DeGroot, M. H. 1969. Optimal Statistical Decisions, McGraw-Hill Book Company, New York
Dourson, M. L. and Stara, J. F. 1983. Regulatory history and experimental support of uncertainty (safety factors). Regulatory Toxicology and Pharmacology, 3: 224–38
Draper, D. 1995. Assessment and propagation of model uncertainty. Journal Royal Statistical Society, Series B, 57 (1): 45–97
Eddy, D. M., Hasselblad, V., and Shachter, R. 1990. An introduction to a Bayesian method for meta-analysis: The confidence profile method. Medical Decision Making, 10 (1): 15–23
Eisenberg, J. N. S., and McKone, T. E. 1998. Decision tree method for the classification of chemical pollutants: Incorporation of across-chemical variability and within-chemical uncertainty. Environmental Science and Technology, 32 (21): 3396–404
Evans, J. S. 1985. The value of improved exposure estimates: A decision analytic approach, Proceedings of the 78th Annual Meeting of the Air Pollution Control Association (June 16–21, 1985), Detroit, Michigan
Evans, J. S., Graham, J. D., Gray, G. M., and Sielken, R. L. 1994a. A distributional approach to characterizing low-dose cancer risk. Risk Analysis, 14 (1): 25–34
Evans, J. S., Gray, G. M., Sielken, R. L., Smith, A. E., Valdez-Flores, C., and Graham, J. D. 1994b. Use of probabilistic expert judgment in distributional analysis of carcinogenic potency, Reg Tox and Pharm, 20: 15–36
Evans, J., Hawkins, N., and Graham, J. 1988. The value of monitoring for radon in the home: A decision analysis, Journal of the Air Pollution Control Association, 38 (11): 1380–5
Evans, J. S. 1985. The value of improved exposure estimates: A decision analytic approach, Proceedings of the 78thAnnual Meeting of the Air Pollution Control Association, (June 16–21, 1985), Detroit, Michigan
Ferson, S. 1996. What Monte Carlo methods can not do. Human and Ecological Risk Assessment, 2: 990–1007
Ferson, S., Ginzburg, L., and Akcakaya, R. Whereof one cannot speak: When input distributions are unknown. Unpublished (apparently) Risk Analysis
Finkel, A. 1990. Confronting Uncertainty in Risk Management: A Guide for Decision Makers. Center for Risk Management, Resources for the Future, Washington, DC
Finkel, A. M., and Evans, J. S. 1987. Evaluating the benefits of uncertainty reduction in environmental health risk management. J Air Pollution Control Association, 37: 1164–71
Fischhoff, B., Riley, D., Kovacs, D. C., and Small, M. 1998. What information belongs in a warning?Psychology and Marketing, 15 (7): 663–86
Fischhoff, B., Slovic, P., and Lichtenstein, S. 1982. Lay foibles and expert fables in judgments about risk. American Statistician, 36: 240–55
Freudenburg, W. 1988. Perceived risk, real risk: Social science and the art of probabilistic risk assessment. Science, 241: 44–9
Frey, H. C. 1992. Quantitative Analysis of Uncertainty and Variability in Environmental Policy Making. American Association for the Advancement of Science, Washington, DC
Frey, H. C., and Burmaster, D. F. 1999. Methods for characterizing variability and uncertainty: Comparison of bootstrap simulation and likelihood-based approaches. Risk Analysis, 19 (1): 109–30
Frey, H. C., and Rhodes, D. S. 1996. Characterization and simulation of uncertain frequency distributions: Effects of distribution choice, variability, uncertainty, and parameter dependence. Human and Ecological Risk Assessment, 4 (2): 423–68
Gee. D. 1997. Criteria for Managing Uncertainty and Regulation in Public Policy. Draft manuscript
Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. 1995. Bayesian Data Analysis. Chapman & Hall, London
Gentle, J. 1998. Random Number Generation and Monte Carlo Methods. Springer-Verlag, Heidelberg
Giering, E. W., and Kandel, A. 1983. The application of fuzzy set theory to the modeling of competition in ecological systems. Fuzzy Sets and Systems, 9: 103–27
Goldfarb, T. D. 2000. Environmental Studies. Dushkin McGraw-Hill, Guilford, CT
Good, I. J. 1959. Kinds of probability. Science, 129: 443–7
Gurian, P. L., Small, M. J., Lockwood III, J. R., and Schervish, M. J. 2001a. Benefit-cost estimation for alternative drinking water maximum contaminant levels. Water Resources Research, 37 (9): 2213–26
Gurian, P. L., Small, M. J., Lockwood III, J. R., and Schervish, M. J. 2001b. Addressing uncertainty and conflicting cost estimates in revising the arsenic MCL. Environmental Science & Technology, 35 (22): 4414–20
Haas, C. N. 1999. On modeling correlated random variables in risk assessment. Risk Analysis, 19 (6): 1205–14
Habicht, H. 1992. Guidance on Risk Characterization for Risk Managers and Risk Assessors. USEPA memorandum to Assistant and Regional Administrators
Haimes, Y. Y., and Lambert, J. 1994. When and how can you specify a probability distribution when you don't know much, Risk Analysis, 14 (5): 661–706
Hammitt, J. K., and Shlyakhter, A. I. 1999. The expected value of information and the probability of surprise. Risk Analysis, 19 (1): 135–52
Henrion, M. 1982. The value of knowing how little you know: The advantages of probabilistic treatment in policy analysis, Ph.D. dissertation, Carnegie-Mellon University, Pittsburgh
Henrion, M., and Fischhoff, B. 1986. Assessing uncertainty in physical constants. American Journal of Physics, 54 (9): 791–8
Hertwich, E. G., McKone, T. E., and Pease, W. S. 1999. Parameter uncertainty and variability in evaluative fate and exposure models. Risk Analysis, 19: 1193–1204
Hilton, R. W. 1981. The determinants of information value: Synthesizing some general results. Management Science, 27 (1): 57–64
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 (5): 707–12
Hunt, S., Frewer, L. J., and Shepard, R. 1999. Public trust in sources of information about radiation risks in the UK. Journal of Risk Research, 2: 167–80
Iman, R. L., and Conover, W. J. 1982. A distribution-free approach to inducing rank correlation among input variables. Communications in Statistics, B11 (3): 311–34
Iman, R. L., and Hora, S. C. 1989. Bayesian methods for modeling recovery times with an application to the loss of off-site power at nuclear power plants. Risk Analysis, 9 (1): 25–36
IPCC (Intergovernmental Panel on Climate Change). 1995. Impacts, Adaptations and Mitigation of Climate Change: Scientific-Technical Analyses Contribution of Working Group II to the Second Assessment of the Intergovernmental Panel on Climate Change, R. T. Watson, M. C. Zinyowera, and R. H. Moss, eds. Cambridge University Press, Cambridge
IPCC (Intergovernmental Panel on Climate Change). 2001a. Climate Change 2001: The Scientific Basis. See
IPCC (Intergovernmental Panel on Climate Change). 2001b. Climate Change 2001: Impacts, Adaptation and Vulnerability. See
IPCC (Intergovernmental Panel on Climate Change). 2001c. Climate Change 2001: Mitigation. See
Isukapalli, S. S., and Georgopoulos, P. G. 2001. Computational Methods for Sensitivity and Uncertainty Analysis for Environmental and Biological Models. Project Report to U.S. EPA Office of Research and Development (ORD) National Exposure Research Laboratory. EPA/600/R-01-068. Research Triangle Park, NC
Jasanoff, S. 1987. Cultural aspects of risk assessment in Britain and the United States. In B. B. Johnson and V. T. Covello, eds., The Social and Cultural Construction of Risk, pp. 359–97. Reidel, Dordrecht, Netherlands
Jasanoff, S. 1990. The Fifth Branch, Science Advisers as Policymakers. Harvard University Press, Cambridge, MA
Jasanoff, S. 1993. Bridging the two cultures of risk analysis. Risk Analysis, 13: 123–9
Johnson, B. B., and Slovic, P. 1995. Presenting uncertainty in health risk assessment: Initial studies of its effects on risk perception and trust. Risk Analysis, 15: 485–94
Johnson, R., Pankow, J., Bender, D., Price, C., and Zogorski, J. 2000. MTBE: To what extent will past releases contaminate community water supply wells?ES&T, 34 (9): 210A–217A
Julien, B., Fenves, S. J., and Small, M. J. 1992. Knowledge acquisition methods for environmental evaluation. AI Applications, 6: 1–20
Kadane, J. B., and Wolfson, L. J. 1998. Experiences in elicitation. Journal of the Royal Statistical Society, Series D, 47: 3–19 (with discussion)
Kahneman, D., Slovic, P., and Tversky, A. 1982. Judgment under Uncertainty: Heuristics and Biases. Cambridge University Press, New York
Kalagnanam, J., and Diwekar, U. 1997. An efficient sampling technique for off-line quality control, Technometrics, 38: 308
Kammen, D. M., and Hassenzahl, D. M. 1999. Should We Risk It? Exploring Environmental, Health, and Technological Problem Solving, Princeton University Press, Princeton, NJ
Kasperson, R. E., and Kasperson, J. X. 1996. The social amplification and attenuation of risk. Annals of the American Academy of Political and Social Sciences, 545: 95–105
Kasperson, R., Renn, O., Slovic, P., Brown, H., Emel, J., Goble, R., Kasperson, J., and Ratick, S. 1988. The social amplification of risk: A conceptual framework. Risk Analysis, 8: 177–87
Keeney, R. L. 1982. Decision analysis: An overview. Operations Research, 39: 803–38
Klir, G. J., and Folger, T. A. 1988. Fuzzy Sets, Uncertainty, and Information, Prentice Hall, Englewood Cliffs, NJ
Larkin, L. I. 1985. A fuzzy logic controller for aircraft flight control. In M. Sugeno, ed., Industrial Applications of Fuzzy Control. North-Holland, New York
Lave, L. 1978. “Eight Frameworks of Regulation: The Strategy of Social Regulation,” Brookings Institute, pp. 8–28
Lave, L. B., Resendiz-Carrillo, D., and McMichael, F. C. 1990. Safety goals for high-hazard dams: Are dams too safe?Water Resources Research, 26 (7): 1383–91
Lee, P. M. 1989. Bayesian Statistics: An Introduction, Oxford University Press, Oxford
Lempert, R., Schlesinger, M., and Bankes, S. 1996. When we don't know the costs or the benefits: Adaptive strategies for abating climate change. Climactic Change, 33: 235–74
Levin, A., Fratt, D. B., Leonard, A., et al.1991. Comparative analysis of health risk assessments for muncipal waste combustors. Journal of the Air and Waste Management Association, 41 (1): 20–31
Lewis, H. W., Budnitz, R. J., Kouts, H. J. C., Lowenstein, W. B., Rowe, W. D., Von Hippel, F., and Zachariasen, F. 1979. Risk Assessment Review Group Report to theU.S.Nuclear Regulatory Commission. NUREG/CR-0400
Lichtenstein, S., and Fischhoff, B. 1977. Do those who know more also know more about how much they know?Organizational Behavior and Human Performance, 20: 159–83
Lockwood III, J. R., Schervish, M. J., Gurian, P., and Small, M. H. 2001. Characterization of arsenic occurrence in US drinking water treatment facility source waters. Journal of American Statistical Association, 96: 456, pp. 1184–1193
MacKenzie, D. 1990. Inventing Accuracy: A Historical Sociology of Nuclear Missile Guidance. MIT Press, Cambridge, MA
March, J. G., and Simon, H. A. 1958. Organizations. John Wiley and Sons, New York
McElhany, P., Ruckelshaus, M., Ford, M. J., Wainwright, T., and Bjorkstedt, E. 2000. Viable Salmonid Populations and the Recovery of Evolutionarily Significant Units. National Marine Fisheries Service
McKay, M. D., Conover, W. J., and Beckman, R. J. 1979. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21 (2): 239–45
McKone, T. E., and Bogen, K. T. 1992. Uncertainties in health-risk assessment: An integrated case study based on tetrachloroethylene in California groundwater. Regulatory Toxicology and Pharmacology, 15: 86–103
Merkhofer, M. W. 1987. Quantifying judgmental uncertainty: Methodology, experiences, and insights. IEEE Transactions on Systems, Man, and Cybernetics. 17 (5): 741–52
Merz, J., Small, M. J., and Fischbeck, P. 1992. Measuring decision sensitivity: A combined Monte Carlo-logistic regression approach. Medical Decision Making, 12: 189–96
Morgan, M. G., and Dowlatabadi, H. 1996. Learning from integrated assessment of climate change. Climatic Change, 34 (3–4): 337–68
Morgan, M. G., and Henrion, M. 1990. Uncertainty: A Guide for Dealing with Uncertainty in Quantitative Risk and Policy Analysis. Cambridge University Press, Cambridge
Morgan, M. G., Fischhoff, B., Bostrom, A., Lave, L., and Atman, C. 1992. Communicating risk to the public. Environmental Science and Technology, 26 (11): 2048–56
Morgan, M. G., Henrion, M., and Morris, S. C. 1980, Expert Judgment for Policy Analysis. BNL 51358. Brookhaven National Laboratory. Brookhaven, NY
Morokoff, W. J., and Caflisch, R. E. 1994. Quasi-random sequences and their discrepancies. SIAMJournal on Scientific Computing, 15 (6): 1251–79
Nakatsuyama, M., Nagahashi, H., and Nishizuka, N. 1984. Fuzzy logic phase controller for traffic functions in the one-way arterial road. ProceedingIFAC9thTriennial World Congress, pp. 2865–70, Pergamon Press, Oxford
NAS. 1987. Report on the Delaney Paradox. National Academics Press. Washington, DC
NCRP. 1996. A Guide for Uncertainty Analysis in Dose and Risk Assessments Related to Environmental Contamination. National Council on Radiation Protection and Measurements. NCRP Commentary No. 14. Bethesda, MD
Norsys. 1998. Netica™ Application for Belief Networks and Influence Diagrams: User's Guide, Versions 1.03 for Macintosh and 1.05 for Windows. Norsys Software Corporation, Vancouver, BC, Canada
NRC. 1975. Reactor Safety Study: An Assessment of Accident Risks inU.S.Commercial Nuclear Power Plants. WASH-1400/NUREG 751014. U.S. Nuclear Regulatory Commission, Washington, DC
NRC. 1983. Risk Assessment in the Federal Government: Managing the Process (also known as “The Red Book”). National Academy Press, Washington, DC
NRC. 1994. Science and Judgement in Risk Assessment. National Academy Press, Washington, DC
NRC. 1996. Understanding Risk: Informing Decisions in a Democratic Society. National Academy Press, Washington, DC
NRC. 1999. Our Common Journey: A Transition Toward Sustainability, Board on Sustainable Development, National Research Council, National Academy Press, Washington, DC
NRC. 2000. Incorporating Science, Economics, and Sociology in Developing Sanitary and Phytosanitary Standards in International Trade, Proceedings of a Conference. National Research Council, National Academy Press, Washington, DC
Pate, E. 1983. Acceptable decision processes and acceptable risks in public sector regulations. IEEE Transactions on Systems, Man, and Cybernetics, SMC-13: 113–24
Pate-Cornell, E. M. 1996. Uncertainties in risk analysis: Six levels of treatment. Reliability Engineering and System Safety, 54: 95–111
Patt, A. 1999. Extreme outcomes: The strategic treatment of low probability events in scientific assessments. Risk, Decision, and Policy, 4 (1): 1–15
Pearl, J. 1988. Probabilistic Reasoning in Intelligent Systems. Morgan Kaufman, San Mateo, CA
Peters, R. G., Covello, V. T., and McCallum, D. B. 1997. The determinants of trust and credibility in environmental risk communication: An empirical study. Risk Analysis, 17: 43–54
Petts, J. 1998. Trust and waste management information expectation versus observation. Journal of Risk Research, 1: 307–20
Press, S. J. 1989. Bayesian Statistics: Principles, Models, and Applications. Wiley, New York
Raffensperger, C., and Tickner, J. A., eds. 1999. Protecting Public Health and the Environment – Implementing the Precautionary Principle. Island Press, Washington, DC
Raiffa, H. 1968. Decision Analysis: Introductory Lectures on Choices Under Uncertainty. Addison-Wesley Publishing, Reading, MA
Raiffa, H., and Schlaifer, R.O. 1961. Applied Statistical Decision Theory, Harvard University Press, Cambridge, MA
Ramsey, F. P. 1931. The Foundation of Mathematics and Other Logical Essays. Kegan Paul, London
Renn, O., Burns, W. J., Kasperson, J. X., Kasperson, R. E., and Slovic, P. 1992. The social amplification of risk: Theroetical foundations and empirical applications. Journal of Social Issues, 48: 127–60
Shlyakhter, A. I. 1994. “Improved Framework for Uncertainty Analysis: Accounting for Unsuspected Errors,” Risk Analysis, 14: 441–7
Simon, T. W. 1999. Two dimensional Monte Carlo simulation and beyond: A comparison of several probabilistic risk assessment methods applied to a Superfund site. Human and Ecological Risk Assessment, 5 (4): 823–43
Slovic, P. 1993. Perceived risk, trust, and democracy. Risk Analysis, 13: 675–82
Slovic, P., Fischoff, B., and Lichtenstein, S. 1979. Rating the risks. Environment, 21: 14–20, 36–9
Small, M. J., and Fischbeck, P. F. 1999. False precision in Bayesian updating with incomplete models. Human and Ecological Risk Assessment, 5 (2): 291–304
Smith, A. E., Ryan, P. B., and Evans, J. S. 1992. The effect of neglecting correlations when propagating uncertainty and estimating the population distribution of risk. Risk Analysis, 12: 467–74
Solow, A. R., Adams, R. F., Bryant, K. J., Legler, D. M., O'Brien, J. J., McCarl, B. A., Nayda, W., and Weiher, R. 1998. The value of improved ENSO prediction to U.S. agriculture. Climatic Change, 39: 47–60
Song, X.-H., and Hopke, P. K. 1996. Solving the chemical mass balance problem using an artificial neural network. Environmental Science & Technology, 30 (2): 531–5
Spensley, J. W. 1995. National Environmental Policy Act. In T. F. P. Sullivan, ed., Environmental Law Handbook, 13th ed., Chapter 10. Government Institutes, Rockville, MD
Spetzler, C. S., and Holstein, S. 1975. Probability encoding in decision analysis. Management Science, 22 (3): 340–58
Squillace, P. J., Zogorski, J. S., Wilber, W. G., and Price, C. V. 1996. Preliminary assessment of the occurrence and possible sources of MTBE in groundwater in the United States, 1993–1994. Environmental Science and Technology, 30 (5): 1721–30
Stiber, N. A., Pantazidou, M., and Small, M. J. 1999. Expert system methodology for evaluating reductive dechlorination at TCE sites. ES&T, 33 (17): 3012–20
Taylor, A. C. 1993. Using objective and subjective information to generate distributions for probabilistic exposure assessment. Journal of Exposure Analysis and Environmental Epidemiology, 3: 285–98
Taylor, A., Evans, J., and McKone, T. 1993. The value of animal test information in environmental control decisions. Risk Analysis, 13: 403–12
Tezuka, S. 1995. Uniform Random Numbers: Theory and Practice. Kluwer Academic Publishers, Dordrecht
Thompson, K. M. 1999. Developing univariate distributions from data for risk analysis. Human and Ecological Risk Assessment, 5 (4): 755–83
Thompson, K. M., and Evans, J. S. 1997. The value of improved exposure information for perchlorethylene (Perc): A case study for dry cleaners. Risk Analysis, 17 (2): 253–71
Thompson, K. M., and Graham, J. D. 1996. Going beyond the single number: Using probabilistic risk assessment to improve risk management. Human and Ecological Risk Assessment, 2 (4): 1008–34
Thompson, P. B., and Dean, W. 1996. Competing conceptions of risk. Risk: Health, Safety & Environment, 7: 361–84
Tickner, J. A. 1999. A map toward precautionary decision making. In C. Raffensperger and J. A. Tickner, eds., Protecting Public Health and the Environment – Implementing the Precautionary Principle. Island Press, Washington, DC
UCC Commission for Racial Justice. 1987. Toxic Wastes and Race in the United States. United Church of Christ and Public Data Access, New York
UK-ILGRA. 1996. Use of Risk Assessment within Government Departments. UK Health and Safety Executive, HSE Books, Sudbury, Suffolk, UK. See also
UK-ILGRA. 1999. Risk Assessment and Risk Management – Improving Policy and Practice within Government Departments. UK Health and Safety Executive, HSE Books, Sudbury, Suffolk, UK
U.S. CEQ. 1971. Environmental Quality. GPO, Washington, DC
U.S. EPA Science Advisory Board. 1995. Beyond the Horizon: Using Foresight to Protect the Environmental Future. USEPA Science Advisory Board, Washington, DC
U.S. EPA National Center for Environmental Assessment. 1997a. Exposure Factors Handbook, NTIS: PB98-124217, See also, Washington, DC
U.S. EPA Science Policy Council. 1997b. Proposed Policy for Use of Monte Carlo Analysis in Agency Risk Assessment. Memorandum of William P. Wood, Executive Director, Risk Assessment Forum, to Dorothy E. Patton, Executive Director of Science Policy Council (8104), January 29, 1997
U.S. EPA Risk Assessment Forum. 1998. Report of the Workshop on Selecting Input Distributions for Probabilistic Assessments. Prepared by Eastern Research Group, Inc., for EPA under EPA Contract No. 68-D5-0028, Washington, DC
U.S. EPA Risk Assessment Forum. 1999. Report of the Workshop on Selecting Input Distributions for Probabilistic Assessments USEPA 630/R-98/004. January 1, 1999. U.S. EPA Risk Assessment Forum, Washington, DC
U.S. EPA Office of Research and Development. 2000. Exploratory Research to Anticipate Future Environmental Issues. FY 2000 STAR Program Request for Applications. U.S. EPA ORD National Center for Environmental Research, Washington, DC.
Winkler, R. L. 1967. The assessment of prior distributions in Bayesian analysis. Journal of the American Statistical Association, 62: 776–800
Wiser, G. 2002. Analysis and perspective: Kyoto Protocol packs powerful implementation punch. International Reporter Current Report, 25 (2): 86. See
Wolfson, L. J. 1995. Elicitation of Priors and Utilities for Bayesian Analysis. PhD Thesis, Department of Statistics, Carnegie Mellon University, Pittsburgh
Wolfson, L. J., Kadane, J. B., and Small, M. J. 1996. Bayesian environmental policy decisions: Two case studies. Ecological Applications, 6 (4): 1056–66
Wolpert, R. L. 1989. Eliciting and combining subjective judgments about uncertainty. International Journal of Technology Assessment in Health Care, 5 (4): 537–57
Wood, E. F., and Rodriguez-Iturbe, I. 1975. Bayesian inference and decision making for extreme hydrologic events. Water Resources Research, 11 (4): 533–42
Word, C. J., Harding, A. K., Bilyard, G. R., and Weber, J. R. 1999. Basic science and risk communication: A dialogue-based study. Risk: Health Safety and Environment, 10 (2), 231–42
World Watch Institute. 2000. State of the World. Norton, New York
Wynne, B. 1980. Technology, risk and participation: The social treatment of uncertainty. In J. Conrad, ed., Society, Technology and Risk, pp. 83–107. Academic Press, New York
Wynne, B. 1987. Risk Management and Hazardous Wastes: Implementation and the Dialectics of Credibility. Springer, Berlin
For further reading
Bedford, T., and Cooke, R. 2001. Probabilistic Risk Analysis: Foundations and Methods, Cambridge University Press, Cambridge
Covello, V. T., and Merkhofer, M. W. 1993. Risk Assessment Methods: Approaches for Assessing Health and Environmental Risks. Plenum Press, New York
Crawford-Brown, D. J. 1999. Risk-Based Environmental Decisions: Methods and Culture. Kluwer Academic Publishers, Boston
Cullen, A. C., and Frey, H. C. 1999. Probabilistic Techniques in Exposure Assessment: A Handbook for Dealing With Variability and Uncertainty in Models and Inputs. Plenum Press, New York
Jaeger, C. C., Renn, O., Rosa, E. A., and Webler, T. 2001. Rational Action, Risk, and Uncertainty. Earthscan, London
Kadane, J. B., and Wolfson, L. J. 1998. Experiences in elicitation. Journal of the Royal Statistical Society D, 47: 3–19 (with discussion)
Kammen, D. M., and Hassenzahl, D. M. 1999. Should We Risk It? Exploring Environmental, Health, and Technological Problem Solving, Princeton University Press, Princeton, NJ
Klapp, M. G. 1992. Bargaining With Uncertainty: Decision-Making in Public Health, Technologial Safety, and Environmental Quality. Auburn House, Dover, MA
Morgan, M. G., and Henrion, M. 1990. Uncertainty: A Guide for Dealing with Uncertainty in Quantitative Risk and Policy Analysis, Cambridge University Press, Cambridge
Porter, T. M. 1995. Trust in Numbers: The Pursuit of Objectivity in Science and Public Life, Princeton University Press, Princeton, NJ
Slovic, P. 2000. The Perception of Risk. Earthscan, London
Stirling, A. 1999. On Science and Precaution in the Management of Technological Risk: Volume I. A Synthesis Report of Case Studies. Report EUR 19056/EN. European Commission for Prospective Technological Studies, Seville, Spain
Stirling, A. 2002. On Science and Precaution in the Management of Technological Risk: Volume II. Case Studies. Report EUR 19056/EN/2. European Commission for Prospective Technological Studies, Seville, Spain
Warren-Hicks, W. H., and Moore, D. R. J., eds. 1998. Uncertainty Analysis in Ecological Risk Assessment. Society of Environmental Toxicology and Chemistry (SETAC), Pensacola, FL