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Imprecise Probability

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International Encyclopedia of Statistical Science

Overview

Quantification of uncertainty is mostly done by the use of precise probabilities: for each event A, a single (classical, precise) probability P(A) is used, typically satisfying Kolmogorov’s axioms (Augustin and Cattaneo 2010). Whilst this has been very successful in many applications, it has long been recognized to have severe limitations. Classical probability requires a very high level of precision and consistency of information, and thus it is often too restrictive to cope carefully with the multi-dimensional nature of uncertainty. Perhaps the most straightforward restriction is that the quality of underlying knowledge cannot be adequately represented using a single probability measure. An increasingly popular and successful generalization is available through the use of lower and upper probabilities, denoted by P(A) and \(\overline{P}(A)\) respectively, with \(0 \leq \underline{P}(A) \leq \overline{P}(A) \leq 1\), or, more generally, by lower and upper expectations...

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Author information

Authors and Affiliations

  1. Durham University, Durham, UK

    Frank P. A. Coolen & Matthias C. M. Troffaes

  2. Ludwig Maximilians University, Munich, Germany

    Thomas Augustin

Authors
  1. Frank P. A. Coolen
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  2. Matthias C. M. Troffaes
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  3. Thomas Augustin
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Editor information

Editors and Affiliations

  1. Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia

    Miodrag Lovric

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© 2011 Springer-Verlag Berlin Heidelberg

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Coolen, F.P., Troffaes, M.C., Augustin, T. (2011). Imprecise Probability. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_296

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