Large Deviations Theory
In probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. Some basic ideas of the theory can be tracked back to Laplace and Cramér, although a clear unified formal definition was introduced in 1966 by Varadhan. Large deviations theory formalizes the heuristic ideas of concentration of measures and widely generalizes the notion of convergence of probability measures.
Roughly speaking, large deviations theory concerns itself with the exponential decay of the probability measures of certain kinds of extreme or tail events, as the number of observations grows arbitrarily large.
Read more about Large Deviations Theory: Formal Definition, Brief History, Applications
Famous quotes containing the words large and/or theory:
“Wags try to invent new stories to tell about the legislature, and end by telling the old one about the senator who explained his unaccustomed possession of a large roll of bills by saying that someone pushed it over the transom while he slept. The expression “It came over the transom,” to explain any unusual good fortune, is part of local folklore.”
—For the State of Montana, U.S. public relief program (1935-1943)
“A theory of the middle class: that it is not to be determined by its financial situation but rather by its relation to government. That is, one could shade down from an actual ruling or governing class to a class hopelessly out of relation to government, thinking of gov’t as beyond its control, of itself as wholly controlled by gov’t. Somewhere in between and in gradations is the group that has the sense that gov’t exists for it, and shapes its consciousness accordingly.”
—Lionel Trilling (1905–1975)