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.
Similar content being viewed by others
References
Benford, F.: The Law of Anomalous Numbers, Proceedings of the American Philosophical Society 78 (1938), pp. 551–572.
Berleant, D. and Zhang, J.:UsingCorrelation to Improve Envelopes aroundDerivedDistributions, Reliable Computing 10(1) (2004), to appear,http://class.ee.iastate.edu/berleant/home/.
Chandrakasan, A., Bowhill, W. J., and Fox, F. (eds):Design ofHigh-Performance Microprocessor Circuits, IEEE Press, 2001.
Chang, C.-S.: Performance Guarantees in Communication Networks, Springer-Verlag, 2000.
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.
Cozman, F.: Credal Networks, Artificial Intelligence 120 (2000), pp. 199–233.
Cui, W. C. and Blockley, D. I.: Interval Probability Theory for Evidential Support, International Journal of Intelligent Systems 5 (1990), pp. 183–192.
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.
Dubois, D. and Prade, H.: Possibility Theory: An Approach to Computerized Processing of Uncertainty, Plenum Press, 1988.
Electronic Bulletin of the Rough Set Community, http://www2.cs.uregina.ca/″roughset/.
Fagiuoli, E. and Zaffalon, M.:An Exact Interval Propagation Algorithmfor Polytreeswith Binary Variables, Artificial Intelligence 106(1) (1998), pp. 77–107.
Fuzzy Sets and Systems, Elsevier, http://www.elsevier.nl/locate/fss.
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/.
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.
Hill, T. P.: The Difficulty of Faking Data, Chance 12(3) (1999), pp. 27–31.
Hutchinson, T. P. and Lai, C. D.: Continuous Bivariate Distributions Emphasizing Applications, Rumsby Scientific Publishing, Adelaide, 1990.
International Journal of Approximate Reasoning, Elsevier.
Kolmogoroff, A.: Confidence Limits for an Unknown Distribution Function, Annals of Mathematical Statistics 12 (4) (1941), pp. 461–463.
Kyburg, H. E.: Interval-Valued Probabilities, http://ippserv.rug.ac.be/ documentation/interval prob/interval prob.html (as of 6/03).
Kyberg, H. E. and Pittarelli, M.: Set-Based Bayesianism, IEEE Trans. On Systems, Man, and Cybernetics 26(3) (1996), pp. 324–339.
Levi, I.: The Enterprise of Knowledge, an Essay on Knowledge, Credal Probabiliy, and Chance, MIT Press, 1980.
Little, R. J. and Rubin, D. B.: Statistical Analysis with Missing Data, Wiley, 1987.
Manski, C. F.: Partial Identification of Probability Distributions, Springer-Verlag, 2003.
Mehrotra, V.: Modeling the Effects of Systematic Process Variation on Circuit Performance, dissertation, MIT, 2001.
Nelsen, R. B.: An Introduction to Copulas, Lecture Notes in Statistics 139, Springer-Verlag, 1999.
Newcomb, S.:Note on the Frequency ofUse of theDifferentDigits inNaturalNumbers, American Journal of Mathematics 4 (1881), pp. 39–40.
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.
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.
The Imprecise Probabilities Project, http://ippserv.rug.ac.be/home/ipp.html.
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.
Wang, Z.: Internet QoS: Architectures and Mechanisms for Quality of Service, Morgan-Kaufmann, 2001.
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).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Issue Date:
DOI: https://doi.org/10.1023/A:1025888503247