10 Mar 2004
CS 3243 - Uncertainty
2
Bayes' Rule
nProduct rule P(aÙb) = P(a | b) P(b) = P(b | a) P(a)
n Þ Bayes' rule: P(a | b) = P(b | a) P(a) / P(b)
n
nor in distribution form
n P(Y|X) = P(X|Y) P(Y) / P(X) = αP(X|Y) P(Y)
n
nUseful for assessing diagnostic probability from causal probability:
nP(Cause|Effect) = P(Effect|Cause) P(Cause) / P(Effect)
n
nE.g., let M be meningitis, S be stiff neck:
nP(m|s) = P(s|m) P(m) / P(s) = 0.5 × 0.0002 / 0.05 = 0.0002
nNote: posterior probability of meningitis still very small!