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What is a likelihood?

  • A.The probability of the hypothesis given the evidence
  • B.The prior probability of the hypothesis being true
  • C.The probability that the hypothesis is likely to hold
  • D.The probability of the evidence given the hypothesis

Answer: D

The likelihood points from hypothesis to evidence, and is usually the direction in which knowledge is available, since one knows how often a disease produces a symptom. Bayes' rule converts it into the posterior, which points the other way and is what a diagnosis requires. Confusing the two is the base rate fallacy in its usual form. That the available knowledge and the wanted conclusion point in opposite directions is precisely why the rule is needed.

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