About: Which Distributions (or Families of Distributions) Best Represent Interval Uncertainty: Case of Permutation-Invariant Criteria

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An Entity of Type : schema:ScholarlyArticle, within Data Space : wasabi.inria.fr associated with source document(s)

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type	Academic Article research paper schema:ScholarlyArticle
isDefinedBy	Covid-on-the-Web dataset
has title	Which Distributions (or Families of Distributions) Best Represent Interval Uncertainty: Case of Permutation-Invariant Criteria
Creator	Beer, Michael Kosheleva, Olga Kreinovich, Vladik Urenda, Julio
Source	PMC
abstract	In many practical situations, we only know the interval containing the quantity of interest, we have no information about the probabilities of different values within this interval. In contrast to the cases when we know the distributions and can thus use Monte-Carlo simulations, processing such interval uncertainty is difficult – crudely speaking, because we need to try all possible distributions on this interval. Sometimes, the problem can be simplified: namely, for estimating the range of values of some characteristics of the distribution, it is possible to select a single distribution (or a small family of distributions) whose analysis provides a good understanding of the situation. The most known case is when we are estimating the largest possible value of Shannon’s entropy: in this case, it is sufficient to consider the uniform distribution on the interval. Interesting, estimating other characteristics leads to the selection of the same uniform distribution: e.g., estimating the largest possible values of generalized entropy or of some sensitivity-related characteristics. In this paper, we provide a general explanation of why uniform distribution appears in different situations – namely, it appears every time we have a permutation-invariant optimization problem with the unique optimum. We also discuss what happens if we have an optimization problem that attains its optimum at several different distributions – this happens, e.g., when we are estimating the smallest possible value of Shannon’s entropy (or of its generalizations).
has issue date	2020-05-18(xsd:dateTime)
bibo:doi	10.1007/978-3-030-50146-4_6
has license	no-cc
sha1sum (hex)	f44f7ed50d4faf7371dafd556a55e95811b086b1
schema:url	https://doi.org/10.1007/978-3-030-50146-4_6
resource representing a document's title	Which Distributions (or Families of Distributions) Best Represent Interval Uncertainty: Case of Permutation-Invariant Criteria
has PubMed Central identifier	PMC7274317
schema:publication	Information Processing and Management of Uncertainty in Knowledge-Based Systems
resource representing a document's body	covid:f44f7ed50d4faf7371dafd556a55e95811b086b1#body_text
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