ML & Math

Bayes' theorem

P(A∣B) = P(B∣A)·P(A)/P(B). The rule for updating belief.


In plain terms

Counterintuitive when P(A) is small: a 99%-accurate test on a 1-in-1000 disease still gives ~9% true-positive rate.

Origin

Thomas Bayes, "An Essay towards solving a Problem in the Doctrine of Chances," published posthumously in 1763 by Richard Price. Underpins every probabilistic ML model.

Where it shows up in production
  • Spam filters Naive Bayes was the default spam classifier in the 2000s. Still a hard baseline to beat.
  • Medical testing intuition A 99% accurate test for a 1-in-1000 disease still gives ~9% true-positive rate — the classic Bayesian counterintuitive example.
On Semicolony
Sources & further reading
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