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State Bayes' theorem and one intuitive use.

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Answer

  • P(A  ∣  B)  =  P(B  ∣  A)P(A\; \mid \;B)\; = \;P(B\; \mid \;A) P(A) / P(B).
  • Intuition: update a prior belief P(A) with new evidence B to get a posterior belief P(A  ∣  B)P(A\; \mid \;B).
  • Classic use: medical testing with base rates.
  • Even a highly sensitive/specific test on a rare disease produces mostly false positives if the disease prevalence is low.
Check yourself — multiple choice
  • P(A∣B)  =  P(A)  +  P(B)P(A \mid B)\; = \;P(A)\; + \;P(B)
  • P(A∣B)  =  P(B∣A)P(A \mid B)\; = \;P(B \mid A) P(A) / P(B)
  • P(A∣B)  =  P(A)  −  P(B)P(A \mid B)\; = \;P(A)\; - \;P(B)
  • Bayes' theorem is a special case of the CLT

Bayes' rule: posterior = likelihood * prior / evidence.

#probability#bayesian

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