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- Upper_and_lower_probabilities 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,[citation needed] 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: see also Choquet(1953).More precisely, in the work of these authors one considers in a power set, , a mass function satisfying the conditionsIn 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 settingThe upper and lower probabilities are also related with probabilistic logic: see Gerla (1994).Observe also that a necessity measure can be seen as a lower probability and a possibility measure can be seen as an upper probability.".
- Upper_and_lower_probabilities wikiPageID "3011778".
- Upper_and_lower_probabilities wikiPageRevisionID "491072322".
- Upper_and_lower_probabilities hasPhotoCollection Upper_and_lower_probabilities.
- Upper_and_lower_probabilities subject Category:Exotic_probabilities.
- Upper_and_lower_probabilities subject Category:Probability_bounds_analysis.
- Upper_and_lower_probabilities 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.Because frequentist statistics disallows metaprobabilities,[citation needed] frequentists have had to propose new solutions.".
- Upper_and_lower_probabilities label "Upper and lower probabilities".
- Upper_and_lower_probabilities sameAs m.08kgn_.
- Upper_and_lower_probabilities sameAs Q7899032.
- Upper_and_lower_probabilities sameAs Q7899032.
- Upper_and_lower_probabilities wasDerivedFrom Upper_and_lower_probabilities?oldid=491072322.
- Upper_and_lower_probabilities isPrimaryTopicOf Upper_and_lower_probabilities.