THE WHATIS.COM WORD-OF-THE-DAY November 28, 2001 Bayesian logic ______________ TODAY'S SPONSOR: Library of Computer & Information Sciences
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Current and possible applications of Bayesian logic include an almost infinite range of research areas, including genetics, astrophysics, psychology, sociology, artificial intelligence (AI), data mining, and computer programming. Bayes first proposed his theorem in his 1763 work (published two years after his death in 1761), An Essay Towards Solving a Problem in the Doctrine of Chances. Bayes' theorem provided, for the first time, a mathematical method that could be used to calculate, given occurrences in prior trials, the likelihood of a target occurrence in future trials. According to Bayesian logic, the only way to quantify a situation with an uncertain outcome is through determining its probability. Bayes' Theorem is a means of quantifying uncertainty. Based on probability theory, the theorem defines a rule for refining an hypothesis by factoring in additional evidence and background information, and leads to a number representing the degree of probability that the hypothesis is true. To demonstrate an application of Bayes' Theorem, suppose that we have a covered basket that contains three balls, each of which may be green or red. In a blind test, we reach in and pull out a red ball. We return the ball to the basket and try again, again pulling out a red ball. Once more, we return the ball to the basket and pull a ball out - red again. We form a hypothesis that all the balls are all, in fact, red. Bayes' Theorem can be used to calculate the probability (p) that all the balls are red (an event labeled as "A") given (symbolized as "|") that all the selections have been red (an event labeled as "B"): p(A|B) = p{A + B}/p{B} Of all the possible combinations (RRR, RRG, RGG, GGG), the chance that all the balls are red is 1/4; in 1/8 of all possible outcomes, all the balls are red AND all the selections are red. Bayes' Theorem calculates the probability that all the balls in the basket are red, given that all the selections have been red as .5 (probabilities are expressed as numbers between 0. and 1., with "1." indicating 100% probability and "0." indicating zero probability). The International Society for Bayesian Analysis (ISBA) was founded in 1992 with the purpose of promoting the application of Bayesian methods to problems in diverse industries and government, as well as throughout the Sciences. The modern incarnation of Bayesian logic has evolved beyond Bayes' initial theorem, developed further by the 18th century French theorist Pierre-Simon de Laplace, and 20th and 21st century practitioners such as Edwin Jaynes, Larry Bretthorst, and Tom Loredo. RELATED TERMS: probability http://whatis.techtarget.com/definition/0,,sid9_gci549076,00.html artificial intelligence http://searchebusiness.techtarget.com/sDefinition/0,,sid19_gci211597,00.html data mining http://searchcrm.techtarget.com/sDefinition/0,,sid11_gci211901,00.html ___________________ SELECTED LINKS ISBA provides more information about Bayesian logic. http://www.bayesian.org/ A research group at Los Alamos National Laboratory offers "A Bayesian Puzzler" that you can try yourself. http://www.strauss.lanl.gov/outgoing/maxent93/twoenvelopes.html Princeton University provides a "Miscellany of Works on Probabilistic Thinking." http://www.princeton.edu/~bayesway/ ____________________________________ (NEW!) 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