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Bayes’ Theorem: Basics

  • Total probability Theorem:


  • Bayes’ Theorem:

\[P(H|X)=\frac{P(X|H)P(H)}{P(X)}=P(X|H)\times P(H)/P(X)\]

    • Let X be a data sample (“evidence”): class label is unknown
    • Let H be a hypothesis that X belongs to class C
    • Classification is to determine P(H|X), (i.e., posteriori probability): the probability that the hypothesis holds given the observed data sample X
    • P(H) (prior probability): the initial probability
      • E.g., X will buy computer, regardless of age, income, …
    • P(X): probability that sample data is observed
    • P(X|H) (likelihood): the probability of observing the sample X, given that the hypothesis holds
      • E.g., Given that X will buy computer, the prob. that X is 31..40, medium income

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