math

Bayes' Theorem Intuition

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Bayes’ theorem tells you how to update your beliefs when you see new evidence.

$$P(H|E) = \frac{P(E|H) \cdot P(H)}{P(E)}$$

In Plain English

  • Start with a belief ($P(H)$, the prior)
  • See evidence ($E$)
  • Update to a new belief ($P(H|E)$, the posterior)

Example

If a test for a rare disease is 99% accurate and you test positive, your chance of having the disease is not 99% — it depends on how rare the disease is. Bayes gives you the real answer.

Always consider the base rate. It is the most commonly ignored factor.