Definition: an array of surmised values of a parameter to be severally explored in the light of a current set of data, with logical symmetry being preserved among all. The merits of each hypothesis entertained are based on quantity, the prior probability. The probability of the data conditional on the hypothesis is computed as the conditional probability for each; the product of the two for each hypothesis is the joint probability, and the ratio of each joint probability to the sum of all the joint probabilities is the posterior probability for that hypothesis. Unlike the Neyman-Pearson test of hypotheses, the answer is a statement about the hypothesis, not about the sample conditional on the hypothesis. No hypothesis is preferred or prevails by default. The procedure may be applied recursively any number of times, as the data becomes available. [Thomas Bayes, British mathematician, 1702–1761]
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