September 2017
Beginner to intermediate
412 pages
8h 55m
English
Content preview from Java Data Analysis
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Bayes' theorem
The conditional probability formula is:
where E and F are any events (that is, sets of outcomes) with positive probabilities. If we swap the names of the two events, we get the equivalent formula:
But F ∩ E = E ∩ F, so P(F ∩ E) = P(E ∩ F) = P(F│E) P(E). Thus:
This formula is called Bayes' theorem. The main idea is that it reverses the conditional relationship, allowing one to compute P(E│F) from P(F│E).
To illustrate Bayes' theorem, suppose ...
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