Bayes Rule
Rev Thomas Bayes
Example P(c)=0.01
90% it is positive if you have c
90% it is negative if you don’t have c
test = positive
probability of having cancer: 8.1/3%
Bayes Rule
prior probability + test evidence -> posterior probability
prior
P(c)=0.01
P(pos|c)=0.9
p(neg|¬c)=0.9
posterior
P(c|Pos)= P(c)*P(Pos|C) = 0.009
P(¬C|Pos)= P(¬C)*P(Pos|¬C) = 0.099
normalize
P(pos)= P(c,Pos)+P(¬C,Pos)=0.108
posterior
P(c|Pos)=0.0833
P(¬c|Pos)=0.9167
This is the algorithm of Bayes Rule
