Reliable Computing

, Volume 9, Issue 6, pp 407–418 | Cite as

Dependable Handling of Uncertainty

  • Daniel Berleant
  • Mei-Peng Cheong
  • Chris Chu
  • Yong Guan
  • Ahmed Kamal
  • Gerald Shedblé
  • Scott Ferson
  • James F. Peters
Article

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Benford, F.: The Law of Anomalous Numbers, Proceedings of the American Philosophical Society 78 (1938), pp. 551–572.Google Scholar
  2. 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/.Google Scholar
  3. 3.
    Chandrakasan, A., Bowhill, W. J., and Fox, F. (eds):Design ofHigh-Performance Microprocessor Circuits, IEEE Press, 2001.Google Scholar
  4. 4.
    Chang, C.-S.: Performance Guarantees in Communication Networks, Springer-Verlag, 2000.Google Scholar
  5. 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. 6.
    Cozman, F.: Credal Networks, Artificial Intelligence 120 (2000), pp. 199–233.Google Scholar
  7. 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. 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. 9.
    Dubois, D. and Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press, 1988.Google Scholar
  10. 10.
    Electronic Bulletin of the Rough Set Community, http://www2.cs.uregina.ca/″roughset/.Google Scholar
  11. 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. 12.
    Fuzzy Sets and Systems, Elsevier, http://www.elsevier.nl/locate/fss.Google Scholar
  13. 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/.Google Scholar
  14. 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. 15.
    Hill, T. P.: The Difficulty of Faking Data, Chance 12(3) (1999), pp. 27–31.Google Scholar
  16. 16.
    Hutchinson, T. P. and Lai, C. D.: Continuous Bivariate Distributions Emphasizing Applications, Rumsby Scientific Publishing, Adelaide, 1990.Google Scholar
  17. 17.
    International Journal of Approximate Reasoning, Elsevier.Google Scholar
  18. 18.
    Kolmogoroff, A.: Confidence Limits for an Unknown Distribution Function, Annals of Mathematical Statistics 12 (4) (1941), pp. 461–463.Google Scholar
  19. 19.
    Kyburg, H. E.: Interval-Valued Probabilities, http://ippserv.rug.ac.be/ documentation/interval prob/interval prob.html (as of 6/03).Google Scholar
  20. 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. 21.
    Levi, I.: The Enterprise of Knowledge, an Essay on Knowledge, Credal Probabiliy, and Chance, MIT Press, 1980.Google Scholar
  22. 22.
    Little, R. J. and Rubin, D. B.: Statistical Analysis with Missing Data, Wiley, 1987.Google Scholar
  23. 23.
    Manski, C. F.: Partial Identification of Probability Distributions, Springer-Verlag, 2003.Google Scholar
  24. 24.
    Mehrotra, V.: Modeling the Effects of Systematic Process Variation on Circuit Performance, dissertation, MIT, 2001.Google Scholar
  25. 25.
    Nelsen, R. B.: An Introduction to Copulas, Lecture Notes in Statistics 139, Springer-Verlag, 1999.Google Scholar
  26. 26.
    Newcomb, S.:Note on the Frequency ofUse of theDifferentDigits inNaturalNumbers, American Journal of Mathematics 4 (1881), pp. 39–40.Google Scholar
  27. 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.Google Scholar
  28. 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.Google Scholar
  29. 29.
    The Imprecise Probabilities Project, http://ippserv.rug.ac.be/home/ipp.html.Google Scholar
  30. 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. 31.
    Wang, Z.: Internet QoS: Architectures and Mechanisms for Quality of Service, Morgan-Kaufmann, 2001.Google Scholar
  32. 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).Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Daniel Berleant
    • 1
  • Mei-Peng Cheong
    • 1
  • Chris Chu
    • 1
  • Yong Guan
    • 1
  • Ahmed Kamal
    • 1
  • Gerald Shedblé
    • 1
  • Scott Ferson
    • 2
  • James F. Peters
    • 3
  1. 1.Department of Electrical and Computer EngineeringIowa State UniversityAmesUSA
  2. 2.Applied BiomathematicsSetauketUSA
  3. 3.Department of Electrical and Computer EngineeringUniversity of ManitobaWinnipegCanada

Personalised recommendations