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. Probability theory is the mathematical study of probability. ... The word probability derives from the Latin probare (to prove, or to test). ...
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. Statistical regularity has motivated the development of the relative frequency concept of probability. ... Cedric Austen Bardell Smith (February 5, 1917, — January 16, 2002) was a British statistician Categories: Scientist stubs | 1917 births | 2002 deaths ... Arthur Dempster may refer to: Arthur Jeffrey Dempster (1886-1950), physicist at the University of Chicago and Manhattan Project participant Arthur Dempster, mathematician at Princeton University This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... Glenn Shafer authored A Mathematical Theory of Evidence which was published by the Princeton University Press in 1976. ... The Dempster-Shafer theory is a mathematical theory of evidence [SH76] based on belief functions and plausible reasoning, which is used to combine separate pieces of information (evidence) to calculate the probability of an event. ...
There are many formal correspondences between upper and lower probability and possibility theory. For example, necessity can be seen as an lower probability and necessity can be seen as an upper probability. Possibility theory is a mathematical theory for dealing with certain types of uncertainty and is an alternative to probability theory. ...
Bayesianism is the philosophical tenet that the mathematical theory of probability applies to the degree of plausibility of a statement.
This is in contrast to frequentism, which rejects degree-of-belief interpretations of mathematical probability, and assigns probabilities only to random events according to their relative frequencies of occurrence.
The Bayesian approach is in contrast to the concept of frequency probability where probability is held to be derived from observed or imagined frequency distributions or proportions of populations.
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