Bridging uncertain and ambiguous knowledge with imprecise probabilities

Environmental Modelling and Software

Volumn 36, Issue , 2012, Pages 122-130

  Rinderknecht, Simon L ^a,b   Borsuk, Mark E ^c   Reichert, Peter ^a,b  

^a SWISS FEDERAL INSTITUTE OF AQUATIC SCIENCE AND TECHNOLOGY   (Switzerland)

^b ETH ZURICH   (Switzerland)

^c DARTMOUTH COLLEGE   (United States)

Author keywords

Density Ratio Class; Expert elicitation; Imprecise probabilities; Intersubjective knowledge; Interval probabilities; Probability box; Qualitative expertise; Quantile class; Quantile elicitation; Quantitative expertise; Robust Bayesian inference; Robust Bayesian statistics; Subjective probabilities

Indexed keywords

BAYESIAN INFERENCE; DENSITY RATIO; EXPERT ELICITATION; IMPRECISE PROBABILITIES; INTERSUBJECTIVE KNOWLEDGE; INTERVAL PROBABILITY; PROBABILITY BOX; QUALITATIVE EXPERTISE; QUANTILE CLASS; QUANTILE ELICITATION; QUANTITATIVE EXPERTISE; ROBUST BAYESIAN STATISTICS; SUBJECTIVE PROBABILITY;

BAYESIAN NETWORKS; DECISION SUPPORT SYSTEMS; INFERENCE ENGINES; PROBABILITY DISTRIBUTIONS;

PROBABILISTIC LOGICS;

BAYESIAN ANALYSIS; DECISION MAKING; DECISION SUPPORT SYSTEM; ENVIRONMENTAL MODELING; LITERATURE REVIEW; NUMERICAL MODEL; PROBABILITY; QUANTITATIVE ANALYSIS; UNCERTAINTY ANALYSIS;

EID: 84861196449     PISSN: 13648152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.envsoft.2011.07.022     Document Type: Article

References (57)

1. Ayyub B.M., Klir G.J. Uncertainty Modeling and Analysis in Engineering and the Sciences 2006, Chapman & Hall.
2. Berger J.O. Robust Bayesian analysis: sensitivity to the prior. Journal of Statistical Planning and Inference 1990, 25:303-328.
3. Berger J.O. An overview of robust Bayesian analysis. Test 1994, 3:5-124.
4. Biggs B.J.F., Stokseth S. Hydraulic habitat suitability for periphyton in rivers. Regulated Rivers-Research & Management 1996, 12(2-3):251-261.
5. Borsuk M.E., Tomassini L. Uncertainty, imprecision, and the precautionary principle in climate change assessment. Water Science and Technology 2005, 52(6):213-225.
6. Borsuk M.E., Powers S.P., Peterson C.H. A survival model of the effects of bottom-water hypoxia on the population density of an estuarine clam (Macoma balthica). Canadian Journal of Fisheries and Aquatic Sciences 2002, 59(8):1266-1274.
7. Camerer C., Weber M. Recent developments in modeling preferences: uncertainty and ambiguity. Journal of Risk and Uncertainty 1992, 5:325-370.
8. Caselton W.F., Luo W.B. Decision-making with imprecise probabilities: Dempster-Shafer theory and application. Water Resources Research 1992, 28(12):3071-3083.
9. Cox R. Probability, frequency and reasonable expectation. American Journal of Physics 1946, 14(1):1-13.
10. de Finetti B. Sul signiflcato soggettivo della probabilità. Fundamenta Mathematicae 1931, 17:298-329.
11. de Finetti B. Theory of probability. A Critical Introductory Treatment 1974, vols. 1 and 2. Wiley, London.
12. DeRobertis L., Hartigan J.A. Bayesian inference using intervals of measures. The Annals of Statistics 1981, 9(2):235-244.
13. Destercke S., Dubois D., Chojnacki E. Unifying practical uncertainty representations: I. generalized p-boxes - II. clouds. International Journal of Approximate Reasoning 2008, 49(3):649-677.
14. Draper D. Assessment and propagation of model uncertainty. Journal of the Royal Statistical Society. Series B (Methodological) 1995, 57(1):45-97.
15. Einhorn H.J., Hogarth R.M. Ambiguity and uncertainty in probabilistic inference. Psychological Review 1985, 92(4):433-461.
16. Ellsberg D. Risk, ambiguity, and the Savage axioms. The Quarterly Journal of Economics 1961, 75(4):643-669.
17. Ferson S., Hajagos J.G. Arithmetic with uncertain numbers: rigorous and (often) best possible answers. Reliability Engineering & System Safety 2004, 85(1-3):135-152.
18. Frisch D., Baron J. Ambiguity and rationality. Journal of Behavioral Decision Making 1988, 1:149-157.
19. Gillies D. Intersubjective probability and confirmation theory. British Journal for the Philosophy of Science 1991, 42:513-533.
20. Howson C., Urbach P. Scientific Reasoning: The Bayesian Approach 1989, Open Court Pub Co.
21. Huber P.J. The case of choquet capacities in statistics. International Statistical Institute 1973, 4:181-188.
22. Ihaka R., Gentleman R. R: a language for data analysis and graphics. Journal of Computational and Graphical Statistics 1996, 5(3):299-314.
23. James A., Low Choy S., Mengersen K. Elicitator: an expert elicitation tool for regression in ecology. Environmental Modelling & Software 2010, 25(1):129-145.
24. Kadane J.B., O'Hagan A. Using finitely additive probability: uniform distributions on the natural numbers. Journal of the American Statistical Association 1995, 90(430):626-631.
25. Kadane J.B., Schervish M.J., Seidenfeld T. Reasoning to a forgone conclusion. Journal of the American Statistical Association 1996, 91(435):1228-1235.
26. Keynes J.M. A Treatise on Probability 1921, Macmillan & Co., Ltd, London.
27. Klir G.J., Wierman M.J. Uncertainty-Based Information 1998, Physica Verlag, New York.
28. Kriegler E., Hall J.W., Held H., Dawson R., Schellnhuber H.J. Imprecise probability assessment of tipping points in the climate system. Proceedings of the National Academy of Sciences 2009, 106(13):5041-5046.
29. Lavine M. An approach to robust Bayesian analysis for multidimensional parameter spaces. Journal of the American Statistical Association 1991, 86(414):400-403.
30. Lavine M. Sensitivity in Bayesian statistics: the prior and the likelihood. Journal of the American Statistical Association 1991, 86(414):396-399.
31. Meyer M.A., Booker J.M. Eliciting and Analyzing Expert Judgment: A Practical Guide 1991, Academic Press Limited, London.
32. Moreno E., Pericchi L.R. Prior assessments for bands of probability measures: empirical Bayes analysis. Test 1993, 2(1-2):101-110.
33. Nordhaus W. Expert opinion on climate change. American Scientist 1994, 82:45-51.
34. O'Hagan A. Probabilitstic uncertainty specification: overview, elaboration techniques and their application to a mechanistic model of carbon flux. Environmental Modelling & Software 2011.
35. O'Hagan A., Buck C.E., Daneshkhah A., Eiser J.R., Garthwaite P.H., Jenkinson D.J., Oakley J.E., Rakow T. Uncertain Judgements. Eliciting Experts' Probabilities 2006, John Wiley, West Sussex, England.
36. O'Hagan A., Oakley J.E. Probability is perfect, but we can't elicit it perfectly. Reliability Engineering & System Safety 2004, 85:239-248.
37. Page T., Heathwaite A.L., Thompson L.J., Pope L., Willows R. Eliciting fuzzy distributions from experts for ranking conceptual risk model components. Environmental Modelling & Software 2011.
38. Parry G.W. The characterization of uncertainty in Probabilistic Risk Assessments of complex systems. Reliability Engineering & System Safety 1996, 54:119-126.
39. Pollino C.A., Woodberry O., Nicholson A., Korb K., Hart B.T. Parameterisation and evaluation of a bayesian network for use in an ecological risk assessment. Environmental Modelling & Software 2007, 22(8):1140-1152.
40. Ramsey F.P. The Foundations of Mathematics and Other Logical Essays 1931, Routledge and Kegan Paul Ltd., London.
41. Refsgaard J.C., van der Sluijs J.P., Højberg A.L., Vanrolleghem P.A. Uncertainty in the environmental modelling process - a framework and guidance. Environmental Modelling & Software 2007, 22(11):1543-1556.
42. Reichert P., Borsuk M.E., Hostmann M., Schweizer S., Spörri C., Tockner K., Truffer B. Concepts of decision support for river rehabilitation. Environmental Modelling & Software 2007, 22(2):188-201.
43. Rinderknecht S.L., Borsuk M.E., Reichert P. Eliciting density ratio classes. International Journal of Approximate Reasoning 2011, 52(6):792-804.
44. Robust Bayesian Analysis 2000, Springer, New York. D. Ríos Insua, F. Ruggeri (Eds.).
45. Savage L. The Foundations of Statistics 1954, John Wiley, New York.
46. Schweizer S. Predicting the Consequences of River Rehabilitation Measures on Morphology, Hydraulics, Periphyton and on Invertebrates 2007, Diss. Nr. 16838, ETHZ, Zürich.
47. Seidenfeld T., Schervish M., Kadane J.B. A representation of partially ordered preferences. Annals of Statistics 1995, 23(6):2168-2217.
48. Shafer G. A Mathematical Theory of Evidence 1976, Princeton University Press, Princeton, NJ.
49. Shannon C. A mathematical theory of communication. Bell System Technical Journal 1948, 27(3 and 4):379-423. 623-656.
50. Von Neumann J., Morgenstern O. Theory of Games and Economic Behavior 1944, Princeton University Press.
51. Walker W.E., Harremoës P., Rotmans J., van der Sluijs J.P., van Asselt M.B.A., Janssen P., Krayer von Krauss M.P. Defining uncetainty. a conceptual basis for uncertainty management in model-based decision support. Integrated Assessment 2003, 4(1):5-17.
52. Walley P. Statistical Reasoning with Imprecise Probabilities 1991, Chapman and Hall, London.
53. Warmink J., Janssen J., Booij M., Krol M. Identification and classification of uncertainties in the application of environmental models. Environmental Modelling & Software 2010, 25(12):1518-1527.
54. Wasserman L. Invariance properties of density ratio priors. The Annals of Statistics 1992, 20(4):2177-2182.
55. Winkler R.L. The assessment of prior distributions in Bayesian analysis. Journal of American Statistical Association 1967, 62(319):776-880.
56. Zadeh L. Fuzzy sets. Information and Control 1965, 8(3):338-353.
57. Zadeh L.A. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1978, 1(1):3-28.