July 2017
Intermediate to advanced
512 pages
13h 21m
English
Content preview from Algebraic and Stochastic Coding Theory
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Bayes’ theorem (Bayes [1764]) is a mathematical statement based on the subjectivists’ notion of belief governed by probability, and it is used to calculate conditional probabilities. In simplest terms, this theorem states that a hypothesis is confirmed by any body of data that its truth renders probable. Thus, the probability of a hypothesis h conditional on some given data d is defined as the ratio of the unconditional probability of the conjunction of the hypothesis with the data to the unconditional probability of the data alone. In other words,
(14.1.1) |
provided that both terms of this ratio exist and p(d) > 0, where pd is a probability function (Birnbaum [1962]), and ∧ denotes ...
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