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Bayes theorem

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Bayes theorem
a statistical means of including local general information, intuitive judgment, clinical skill as learned over a long period, and similar subjective influences, in the assessment of probability, e.g. in making a diagnosis. The formula relates, for example, the conditional probability P(D/S), of a disease (D) being present when a particular sign (S) is observed, to three other probabilities: the prevalence of the disease P(D), the frequency of the sign P(S), and the probability of the sign occurring for the disease P(SD).$${\rm Pr(D\vert S) = {Pr(S\vert D) \times Pr(D)\over Pr(S)}$$


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Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of events, computation of probability of events using permutations and combinations.
Polya explained that the main point of the admittedly somewhat complex Bayes theorem, which has as many as a dozen symbols, is contained in its simple corollary, "A theory is confirmed by its consequences.
 
 
 
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