Bayes' theorem

• Prior odds:

  • O(H) = P(H) / P(¬H) = P(H) / (1 - P(H))

• Likelihood ratio:

  • L(e | H) = P(e | H) / P(e | ¬H)

• Posterior odds:

  • O(H | e) = P(H | e) / P(¬H | e) = L(e | H)O(H)

• Posterior probability:

  • P(H | e) = P(e | H)P(H) / P(e)
    = O(H | e) / (1 + O(H | e))
    

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