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Uncertainty modeling and analysis with intervals: Foundations, tools, applications (Dagstuhl Seminar 11371)

Authors: Isaac E. Elishakoff, Vladik Kreinovich, Wolfram Luther, and Evgenija D. Popova

Published in: Dagstuhl Reports, Volume 1, Issue 9 (2012)

Abstract

This report documents the program and the results of Dagstuhl Seminar 11371 ``Uncertainty modeling and analysis with intervals -- Foundations, tools, applications'', taking place September 11-16, 2011. The major emphasis of the seminar lies on modeling and analyzing uncertainties and propagating them through application systems by using, for example, interval arithmetic.

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Isaac E. Elishakoff, Vladik Kreinovich, Wolfram Luther, and Evgenija D. Popova. Uncertainty modeling and analysis with intervals: Foundations, tools, applications (Dagstuhl Seminar 11371). In Dagstuhl Reports, Volume 1, Issue 9, pp. 26-57, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@Article{elishakoff_et_al:DagRep.1.9.26,
  author =	{Elishakoff, Isaac E. and Kreinovich, Vladik and Luther, Wolfram and Popova, Evgenija D.},
  title =	{{Uncertainty modeling and analysis with intervals: Foundations, tools, applications (Dagstuhl Seminar 11371)}},
  pages =	{26--57},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2011},
  volume =	{1},
  number =	{9},
  editor =	{Elishakoff, Isaac E. and Kreinovich, Vladik and Luther, Wolfram and Popova, Evgenija D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.1.9.26},
  URN =		{urn:nbn:de:0030-drops-33181},
  doi =		{10.4230/DagRep.1.9.26},
  annote =	{Keywords: Uncertainty modeling, Interval arithmetic, Imprecise probabilities, Sensitivity analysis, mechatronics, bioinformatics and finance}
}

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Invited Talk

DOI: 10.4230/OASIcs.CCA.2009.2251

From Interval Computations to Constraint-Related Set Computations: Towards Faster Estimation of Statistics and ODEs under Interval and p-Box Uncertainty (Invited Talk)

Authors: Vladik Kreinovich

Published in: OASIcs, Volume 11, 6th International Conference on Computability and Complexity in Analysis (CCA'09) (2009)

Abstract

Interval computations estimate the uncertainty of the result of data processing in situations in which we only know the upper bounds $\Delta$ on the measurement errors. In this case, based on the measurement result $\widetilde x$, we can only conclude that the actual (unknown) value $x$ of the desired quantity is in the interval $[\widetilde x-\Delta,\widetilde x+\Delta]$. In interval computations, at each intermediate stage of the computation, we have intervals of possible values of the corresponding quantities. As a result, we often have bounds with excess width. To remedy this problem, in our previous papers, we proposed an extension of interval technique to {\it set computations}, where on each stage, in addition to intervals of possible values of the quantities, we also keep sets of possible values of pairs (triples, etc.). In this paper, we show that in several practical problems, such as estimating statistics (variance, correlation, etc.) and solutions to ordinary differential equations (ODEs) with given accuracy, this new formalism enables us to find estimates in feasible (polynomial) time.

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Vladik Kreinovich. From Interval Computations to Constraint-Related Set Computations: Towards Faster Estimation of Statistics and ODEs under Interval and p-Box Uncertainty (Invited Talk). In 6th International Conference on Computability and Complexity in Analysis (CCA'09). Open Access Series in Informatics (OASIcs), Volume 11, pp. 5-16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

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@InProceedings{kreinovich:OASIcs.CCA.2009.2251,
  author =	{Kreinovich, Vladik},
  title =	{{From Interval Computations to Constraint-Related Set Computations: Towards Faster Estimation of Statistics and ODEs under Interval and p-Box Uncertainty}},
  booktitle =	{6th International Conference on Computability and Complexity in Analysis (CCA'09)},
  pages =	{5--16},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-939897-12-5},
  ISSN =	{2190-6807},
  year =	{2009},
  volume =	{11},
  editor =	{Bauer, Andrej and Hertling, Peter and Ko, Ker-I},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.CCA.2009.2251},
  URN =		{urn:nbn:de:0030-drops-22516},
  doi =		{10.4230/OASIcs.CCA.2009.2251},
  annote =	{Keywords: Interval computations, set computations, probability boxes, uncertainty, efficient algorithms}
}

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Documents authored by Kreinovich, Vladik

Uncertainty modeling and analysis with intervals: Foundations, tools, applications (Dagstuhl Seminar 11371)

Abstract

Cite as

From Interval Computations to Constraint-Related Set Computations: Towards Faster Estimation of Statistics and ODEs under Interval and p-Box Uncertainty (Invited Talk)

Abstract

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