10 Mar 2004
CS 3243 - Uncertainty
11
Conditional probability
nConditional or posterior probabilities
ne.g., P(cavity | toothache) = 0.8
ni.e., given that toothache is all I know
n
nNotation for conditional distributions:
nP(cavity | toothache) = 2-element vector of 2-element vectors
n
nIf we know more, e.g., cavity is also given, then we have
nP(cavity | toothache, cavity) = 1
n
nNew evidence may be irrelevant, allowing simplification, e.g.,
nP(cavity | toothache. sunny) = P(cavity | toothache) = 0.8
nThis kind of inference, sanctioned by domain knowledge, is crucial