Information Theory in Risk Analysis
Publication: Journal of Environmental Engineering
Volume 118, Issue 6
Abstract
Risk, or the probability of loss, depends on the amount of information available to predict outcomes, as well as the essentially random characteristics of the process. Probabilities calculated by traditional methods do not reflect information content directly. Therefore, traditional probabilities must be reported along with confidence intervals, particularly in situations in which information is limited. Interpretation of risk—expressed as a degree of confidence in a probability of some loss—is difficult. In this paper, information theory was used to estimate conditional probability distributions, representing risks, for which no data were available but one or two statistics (such as mean values) were known. The resulting distributions expressed information content directly. Revision of these distributions with additional information resulted in narrower distributions, in contrast with traditional approaches. Probabilities of cadmium removal efficiencies experienced for various durations were estimated from knowledge of total annual flow and residue. The complete particle‐size distribution for a sand filter bed was predicted satisfactorily from knowledge of clear water headloss, verifying the method, and providing the basis for a rapid quality‐control test for particle‐size separators.
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References
1.
Amorocho, J., and Espildora, B. (1973). “Entropy in the assessment of uncertainty in hydrologic systems and models.” Water Resour. Res., 9(6).
2.
Barnes, H. H. (1967). “Roughness characteristics of natural channels.” U.S. Geological Survey Water‐Supply Paper 1849. U.S. Geological Survey, Washington, D.C.
3.
Benjamin, J. R., and Cornell, C. A. (1970). Probability, statistics, and decisions for civil engineers. McGraw‐Hill Book Co., New York, N.Y.
4.
Brown, C. B. (1988). “Experiments on disc arrays: coordination and void entropies.” Micromechanics of granular materials. M. Satake, and Jenkins, J. T. (ed.), Elsevier Science Publishers B.V., Amsterdam, The Netherlands, 31–37.
5.
Brown, C. B. (1980). “Entropy constructed probabilities.” J. Engrg. Mech. Div., ASCE, 106(4), 633–640.
6.
Chiu, C.‐L. (1987). “Entropy and probability concepts in hydraulics,” J. Hydr. Engrg., ASCE, 113(5).
7.
Chow, V. T. (1959). Open‐channel hydraulics. McGraw‐Hill Book Co., New York, N.Y.
8.
DeGroot, M. H. (1986). Probability and statistics, 2nd ed., Addison‐Wesley Publishing Co., Reading, Mass.
9.
Erickson, G. J., and Smith, C. R. (eds.). (1988). Maximum‐entropy and Bayesian methods in science and engineering; volume 1: foundations. Kluwer Academic Publishers, Boston, Mass.
10.
Fair, G. M., Geyer, J. C., and Okun, D. A. (1971). Elements of water supply and wastewater disposal, 2d ed. John Wiley and Sons, Inc., New York, N.Y., 410–411.
11.
Hoel, P. G., Port, S. C., and Stone, C. J. (1971). Introduction to probability theory. Houghton Mifflin Co., Boston, Mass.
12.
Jaynes, E. T. (1957a). “Information theory and statistical mechanics, parts I–II.” Physical Reviews, 106(4), 620–630.
13.
Jaynes, E. T. (1957b). “Information theory and statistical mechanics, part II.” Physical Reviews, 108(2), 171–190.
14.
Kapur, J. N. (1983). “Twenty‐five years of maximum‐entropy principle.” J. Mathematical and Physical Sci., 17(2), 103–156.
15.
Leopold, L. B., and Langbein, W. B. (1962). “The concept of entropy in landscape evolution.” Geological Survey Professional Paper 500‐A, U.S. Government Printing Office, Washington, D.C.
16.
Lind, N. C., and Solana, V. (1990). “Fractile constrained entropy estimation of distributions based on scarce data.” Civ. Engrg. Systems, 7(2), 87–93.
17.
“Maximum entropy and Bayesian methods in applied statistics.” (1986). J. H. Justice (ed.), Cambridge University Press, Cambridge, England.
18.
Phien, H. N., and Nguyen, V.‐T.‐V. (1990). “Variances and covariances of the maximum entropy estimates for the pearson type III distribution.” Canadian J. Civ. Engrg., 17(4), 590–596.
19.
Shannon, C. E. (1949). “The mathematical theory of communication.” The Mathematical Theory of Communication. The University of Illinois Press, Urbana, Ill.
20.
Singh, V. P., and Krstanovic, P. F. (1987). “A stochastic model for sediment yield using the principle of maximum entropy.” Water Resour. Res., 23(5), 781–793.
21.
Sonuga, J. O. (1976). “Entropy principle applied to the rainfall‐runoff process.” J. Hydr., 30(1/2), 81–94.
22.
Stedinger, J. R. (1980). “Fitting log normal distributions to hydrologic data.” Water Resour. Res., 16(3).
23.
Tchobanoglous, G., Theisen, H., and Eliassen, R. (1977). Solid wastes: Engineering principles and management issues. McGraw‐Hill Book Co., New York, N.Y.
24.
Tribus, M. (1969). Rational descriptions, decisions and designs. Pergamon Press, New York, N.Y.
25.
Tumeo, M. A., and Orlob, G. T. (1989). “An analytic technique for stochastic analysis in environmental models.” Water Resour. Res., 25(12), 2417–2422.
26.
Van Campenhout, J. M., and Cover, T. M. (1981). “Maximum entropy and conditional probability.” IEEE Trans. on Information Theory, IT‐27(4).
27.
Wastewater engineering; treatment, disposal, and refuse, 3rd Ed. (1991). Rev. by G. Tchobanoglous and F. L. Burton, McGraw‐Hill Book Co., New York, N.Y.
28.
Webber, M. J. (1979). Information theory and urban spatial structure. Croom Helm, London, England.
29.
Willis, R., and Yeh, W. W.‐G. (1987). Groundwater systems planning & management. Prentice‐Hall, Inc., Eriglewood Cliffs, N.J.
30.
Wilson, A. G. (1970). Entropy in urban and regional modeling. Pion Ltd., Methuen, Inc., London, England.
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Copyright © 1992 ASCE.
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Published online: Nov 1, 1992
Published in print: Nov 1992
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