Probabilistic Information Retrieval Probability Basics Recall a few probability basics or events a and b Bayes Rule p(a,b)=p(anb)=p(a bp(b)=p((a p(a bp(b)=p(b ap(ay P(alb)=p(bla)p(a=sp(blapla prior p(b)∑ pbx(x) Posterion x=aa Odds: O(a)=p(a)Probabilistic Information Retrieval 7 Recall a few probability basics ▪ For events a and b: ▪ Bayes’ Rule ▪ Odds:  = = = = =  = = x a a p b x p x p b a p a p b p b a p a p a b p a b p b p b a p a p a b p a b p a b p b p b a p a , ( | ) ( ) ( | ) ( ) ( ) ( | ) ( ) ( | ) ( | ) ( ) ( | ) ( ) ( , ) ( ) ( | ) ( ) ( | ) ( ) 1 ( ) ( ) ( ) ( ) ( ) p a p a p a p a O a − = = Posterior Prior Probability Basics