Get Upper and Lower Probabilities essential facts below. View Videos or join the Upper and Lower Probabilities discussion. Add Upper and Lower Probabilities to your PopFlock.com topic list for future reference or share this resource on social media.
Upper and Lower Probabilities
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:
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