Probability Notation Review

• Prior (unconditional) probability is before evidence is obtained, after is posterior or conditional probability

• P(A) – Prior – only valid when no other info is available• Random variable P(X=pizza), X has a domain <x1, x2,…> and P(xi)=1 (note that variables

are by convention in caps in probability theory)• Probability distribution – P(X) vector (for discrete vars) of probabilities of domain of X.

Sums to 1.• Can use standard connectives, i.e. P(A B)• P(A|B) – conditional probability – probability of A given B• As soon as we know C we should use P(A|B C)• P(A|B) = P(A B)/P(B)• Product rule: P(A B) = P(A|B)P(B) = P(B|A)P(A)• P(A B) = P(A) + P(B) – P(A B) – venn diagram• P(A) + P(!A) = 1• Joint probability table (JPT): Table that shows all of the probabilities for all possible

events

Independence

Independence Disadvantages of the Joint

o Way (way) too big o Hard to gather good stats for

Solution: conditional independence

Conditional Independence Example

B u r g la r y E x a m p le A b u r g la r y o r a n e a r th q u a k e c a n se t o f th e a la r m . I f th e a la r m g o e s o ff , y o u r n e ig h b o r s (J o h n o r

M a r y ) a r e su p p o se d to c a ll y o u . N o te th a t a ll th e r e a so n s fo r w h e n a p e r so n c a lls

a r e n o t g iv e n (c o u ld b e q u ite c o m p le x p o ss ib il it ie s ) , y e t w ill r e p r e se n t c o m p le x c a se w ith a s im p le m o d e l

A la rm

B u rg la ry E a rth q u a k e

M a ry C a llsJ o h n C a lls