Representing and reasoning with probabilities
Bayesian Networks
Joint Distribution
Strom lightning thonder
T, T .25 .20,.05
T, F .40 .04,0.36
F, T .05 .04,0.01
F, F .30 .03,0.27
Random day 2pm – look outside summer
Pr(￢storm) = 0.35
pr(lightning|storm) = .4615 (.25/.65)
X is conditionally independent of Y given Z fi the probability distribution governing X is independent of the value of y given the value of Z; that is, if
P(X=x|Y=y,Z=z)= P(X=x|Z=x)
more compactly write
P(X|Y,Z) = P(X|Z)
sampling
two things distribution are for -probability of value, generate value
simulation of a complex process
approximate inference
P(x)= Σy*P(x,y)
P(x,y)= P(x)*P(y|x)
P(y|x) = P(x|y)*P(y)/P(z)
