Interpretations

Bayesian interpretation

• Probability measures a degree of belief.
• For proposition A and evidence B,
  • P(A), the prior, is the initial degree of belief in A.
  • P(A|B), the posterior, is the degree of belief having accounted for B.
  • the quotient P(B|A)/P(B) represents the support B provides for A.

Frequentist interpretation

• Probability measures a proportion of outcomes.
• For example, suppose an experiment is performed many times.
  • P(A), the proportion of outcomes with property A.
  • P(B), that with property B.
  • P(B|A), the proportion of outcomes with property B out of outcomes with property A.
  • P(A|B), the proportion of those with A out of those with B.