Bayes' theorem

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Related to Bayes rule: conditional probability
  • noun

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(statistics) a theorem describing how the conditional probability of a set of possible causes for a given observed event can be computed from knowledge of the probability of each cause and the conditional probability of the outcome of each cause

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As an example of the use of Bayes rule, suppose that a ball either red or black--is to be drawn from one of two urns.
Bayes Rule is based on the following calculation: There are three out of four chances that urn A
See Appendix B for Bayes' seven definitions that determine the inevitability of the calculation below) Recalling that E is a statement of some evidentiary support Bayes rule proposes: (28)
Given the data observed, application of Bayes rule enables estimation of the posterior distribution of both the size and time of attack, from which summary statistics such as the mean, standard deviation, and probability intervals of the attack size and time are easily estimated.
and application of Bayes rule yields the joint posterior distribution of the size and time of attack as