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Statements

Subject Item: dbr:Probability_box
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:Credal_set
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:Statistical_inference
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:Choquet_integral
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:Dempster–Shafer_theory
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:Possibility_theory
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:Catalog_of_articles_in_probability_theory
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:Imprecise_probability
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:List_of_statistics_articles
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:Probabilistic_logic
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:Superadditivity
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities

Subject Item: dbr:Upper_and_lower_probabilities
rdfs:label: Upper and lower probabilities
rdfs:comment: Upper and lower probabilities are representations of imprecise probability. Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur, this method uses two numbers: the upper probability of the event and the lower probability of the event. In turn, a mass is associated with two non-additive continuous measures called belief and plausibility defined as follows: A different notion of upper and lower probabilities is obtained by the lower and upper envelopes obtained from a class C of probability distributions by setting
dcterms:subject: dbc:Dempster–Shafer_theory dbc:Exotic_probabilities dbc:Probability_bounds_analysis
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dbo:wikiPageWikiLink: dbr:Metaprobability dbr:Glenn_Shafer dbr:Dempster–Shafer_theory dbr:Frequentist_statistics dbc:Exotic_probabilities dbr:Fuzzy_measure_theory dbr:Probability_bounds_analysis dbr:Necessity_measure dbr:Probability_theory dbr:Annals_of_Statistics dbr:Probability dbr:Arthur_P._Dempster dbr:Power_set dbr:Possibility_theory dbr:Imprecise_probability dbr:Cedric_Smith_(statistician) dbr:Probabilistic_logic dbr:Possibility_measure dbr:Interval_finite_element dbc:Probability_bounds_analysis dbc:Dempster–Shafer_theory
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dbo:abstract: Upper and lower probabilities are representations of imprecise probability. Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur, this method uses two numbers: the upper probability of the event and the lower probability of the event. Because frequentist statistics disallows metaprobabilities, frequentists have had to propose new solutions. Cedric Smith and Arthur Dempster each developed a theory of upper and lower probabilities. Glenn Shafer developed Dempster's theory further, and it is now known as Dempster–Shafer theory or Choquet (1953).More precisely, in the work of these authors one considers in a power set, , a mass function satisfying the conditions In turn, a mass is associated with two non-additive continuous measures called belief and plausibility defined as follows: In the case where is infinite there can be such that there is no associated mass function. See p. 36 of Halpern (2003). Probability measures are a special case of belief functions in which the mass function assigns positive mass to singletons of the event space only. A different notion of upper and lower probabilities is obtained by the lower and upper envelopes obtained from a class C of probability distributions by setting The upper and lower probabilities are also related with probabilistic logic: see Gerla (1994). Observe also that a can be seen as a lower probability and a can be seen as an upper probability.
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Subject Item: dbr:Upper_probability
dbo:wikiPageWikiLink: dbr:Upper_and_lower_probabilities
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Subject Item: wikipedia-en:Upper_and_lower_probabilities
foaf:primaryTopic: dbr:Upper_and_lower_probabilities