-
Hypothesis:
$H$ -
Prior probability:
$P(H)$ -
Evidence:
$E$ -
Likelihood:
$P(E|H)$ -
Posterior probability:
$P(H|E)$ -
Bayes' theorem:
$$\text{Posterior}=\text{Prior}\times\text{Likelihood}\div\text{Evidence}$$ $$P(H|E) = {P(H)P(E|H) \over P(E)} = {P(H)P(E|H) \over P(H)P(E|H)+P(\lnot H)P(E|\lnot H)}$$
Bayes theorem, the geometry of changing beliefs - YouTube
-
Hypothesis: One is a librarian
-
Prior probability:
$10\over 210$ -
Evidence: One fits the description,
$4+20 \over 210$ -
Likelihood:
${4\over 10}$ -
Posterior probability:
${4 \over 4+20}$ -
Bayes' theorem:
$${4\over 4+20}={{10\over 210}\times{4\over 10}\over {4+20\over 210}}$$