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Dependable Handling of Uncertainty

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Reliable Computing

Abstract

Uncertainty quantification is an important approach to modeling in the presence of limited information about uncertain quantities. As a result recent years have witnessed a burgeoning body of work in this field. The present paper gives some background, highlights some recent work, and presents some problems and challenges.

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References

  1. Benford, F.: The Law of Anomalous Numbers, Proceedings of the American Philosophical Society 78 (1938), pp. 551–572.

    Google Scholar 

  2. Berleant, D. and Zhang, J.:UsingCorrelation to Improve Envelopes aroundDerivedDistributions, Reliable Computing 10(1) (2004), to appear,http://class.ee.iastate.edu/berleant/home/.

  3. Chandrakasan, A., Bowhill, W. J., and Fox, F. (eds):Design ofHigh-Performance Microprocessor Circuits, IEEE Press, 2001.

  4. Chang, C.-S.: Performance Guarantees in Communication Networks, Springer-Verlag, 2000.

    Google Scholar 

  5. Coolen, F. P. A., Coolen-Schrijner, P., and Yan, K. J.: Nonparametric Predictive Inference in Reliability, Reliability Engineering and System Safety 78 (2002), pp. 185–193.

    Google Scholar 

  6. Cozman, F.: Credal Networks, Artificial Intelligence 120 (2000), pp. 199–233.

    Google Scholar 

  7. Cui, W. C. and Blockley, D. I.: Interval Probability Theory for Evidential Support, International Journal of Intelligent Systems 5 (1990), pp. 183–192.

    Google Scholar 

  8. Davis, J. P. and Hall, J.W.:ASoftware-Supported Process forAssembling Evidence andHandling Uncertainty in Decision-Making, Decision Support Systems 35 (2003), pp. 415–433.

    Google Scholar 

  9. Dubois, D. and Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press, 1988.

  10. Electronic Bulletin of the Rough Set Community, http://www2.cs.uregina.ca/″roughset/.

  11. Fagiuoli, E. and Zaffalon, M.:An Exact Interval Propagation Algorithmfor Polytreeswith Binary Variables, Artificial Intelligence 106(1) (1998), pp. 77–107.

    Google Scholar 

  12. Fuzzy Sets and Systems, Elsevier, http://www.elsevier.nl/locate/fss.

  13. Hampel, F.: Robust Statistics: A Brief Introduction and Overview, Research Report No. 94, Seminar f¨ur Statistik, Edgen¨ossische Technische Hochschule (ETH), Switzerland, 2001, http://stat.ethz.ch/Research-Reports/94.pdf. See also Huber, P. J.: Robust Statistics, Wiley, 1981. See also Int. Conf. on Robust Statistics 2003, http://win-www.uia.ac.be/u/icors03/.

  14. Hill, B. M.: Posterior Distribution of Percentiles: Bayes' Theorem for Sampling from a Population, Journal of the American Statistical Association 63 (1968), pp. 677–691.

    Google Scholar 

  15. Hill, T. P.: The Difficulty of Faking Data, Chance 12(3) (1999), pp. 27–31.

    Google Scholar 

  16. Hutchinson, T. P. and Lai, C. D.: Continuous Bivariate Distributions Emphasizing Applications, Rumsby Scientific Publishing, Adelaide, 1990.

    Google Scholar 

  17. International Journal of Approximate Reasoning, Elsevier.

  18. Kolmogoroff, A.: Confidence Limits for an Unknown Distribution Function, Annals of Mathematical Statistics 12 (4) (1941), pp. 461–463.

    Google Scholar 

  19. Kyburg, H. E.: Interval-Valued Probabilities, http://ippserv.rug.ac.be/ documentation/interval prob/interval prob.html (as of 6/03).

  20. Kyberg, H. E. and Pittarelli, M.: Set-Based Bayesianism, IEEE Trans. On Systems, Man, and Cybernetics 26(3) (1996), pp. 324–339.

    Google Scholar 

  21. Levi, I.: The Enterprise of Knowledge, an Essay on Knowledge, Credal Probabiliy, and Chance, MIT Press, 1980.

  22. Little, R. J. and Rubin, D. B.: Statistical Analysis with Missing Data, Wiley, 1987.

  23. Manski, C. F.: Partial Identification of Probability Distributions, Springer-Verlag, 2003.

  24. Mehrotra, V.: Modeling the Effects of Systematic Process Variation on Circuit Performance, dissertation, MIT, 2001.

  25. Nelsen, R. B.: An Introduction to Copulas, Lecture Notes in Statistics 139, Springer-Verlag, 1999.

  26. Newcomb, S.:Note on the Frequency ofUse of theDifferentDigits inNaturalNumbers, American Journal of Mathematics 4 (1881), pp. 39–40.

    Google Scholar 

  27. Sherwood, H. quoted at http://gro.creditlyonnais.fr/content/rd/home copulas.htm as of 6/03, notes the great, yet often under-recognized overlap among the areas of joint probability distributions with fixed marginals, copulas, doubly stochastic measures, Markov operators, and dependency relations.

  28. Staum, J.: Fundamental Theorems of Asset Pricing for Good Deal Bounds, Mathematical Finance, forthcoming. See also Technical Report 1351, Dept. of ORIE, Cornell University, 2002.

  29. The Imprecise Probabilities Project, http://ippserv.rug.ac.be/home/ipp.html.

  30. Vansteelandt, S. and Goetghebeur, E.: Analyzing the Sensitivity of Generalized Linear Models to Incomplete Outcomes via the IDE Algorithm, Journal of Computational and Graphical Statistics 10(4) (2001), pp. 656–672.

    Google Scholar 

  31. Wang, Z.: Internet QoS: Architectures and Mechanisms for Quality of Service, Morgan-Kaufmann, 2001.

  32. www.gloriamundi.org, gro.creditlyonnais.fr, and www.risklab.ch are sources for reports on mathematical finance, copulas, and related items, including a few mentioning Spearman correlation (as of 6/03).

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Berleant, D., Cheong, MP., Chu, C. et al. Dependable Handling of Uncertainty. Reliable Computing 9, 407–418 (2003). https://doi.org/10.1023/A:1025888503247

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  • DOI: https://doi.org/10.1023/A:1025888503247

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