But Uncertainty is Everywhere. Medical knowledge in logic? Toothache <=> Cavity Problems Too many exceptions to any logical rule Hard to code accurate rules, hard to use them. Doctors have no complete theory for the domain Don’t know the state of a given patient state
A = red spots
B = measles
We know P(A|B),
but want P(B|A).
F F F 0.534
F F T 0.356
F T F 0.006
F T T 0.004
T F F 0.048
T F T 0.012
T T F 0.032
T T T 0.008Conditional Independence
P(A|P,C) = 0.032/(0.032+0.048)
= 0.04 / 0.1 = 0.4
1: Bayes net = representation of a JPD
2: Bayes net = set of cond. independence statements
My house alarm system just sounded (A).
Both an earthquake (E) and a burglary (B) could set it off.
John will probably hear the alarm; if so he’ll call (J).
But sometimes John calls even when the alarm is silent
Mary might hear the alarm and call too (M), but not as reliably
We could be assured a complete and consistent model by fully specifying the joint distribution:
Prob(A, E, B, J, M)
Prob(A, E, B, J, ~M)
Instead of starting with numbers, we will start with structural relationships among the variables
direct causal relationship from Earthquake to Radio
direct causal relationship from Burglar to Alarm
direct causal relationship from Alarm to JohnCall
Earthquake and Burglar tend to occur independently