bayesian - Bayes Learning - MAP hypotesis

Question

Suppose I have a set of hypotesys H = {h1, h2} mutual exclusive. For them P(h1) = 0.2 and p(h3) = 0.3 (prior distribution). Suppose we know also that

P(Y=0 | h1) = 0.2 P(Y=0 | h2) = 0.4

where Y is an attribute (target) that can have two values {1,0}. Suppose finally that you observe the event Y = 0.

Which one is the MAP (Maximum a posteriori) hipotesys?

• MAP is h1
• MAP is h2
• there's no enough element to find MAP
• MAP h1 = MAP h2
• nobody of the possible answer above

Answer 1

Such question should be asked (and now probably migrated) on the math.stackexchange.com or stats.stackexchange.com .

Your question is basic application of the Bayes Theorem

              P(Y=0|h1)P(h1)    0.2*0.2    0.04
P(h1|Y=0) =   -------------   = ------- = ------
                  P(Y=0)         P(Y=0)   P(Y=0)

              P(Y=0|h2)P(h2)    0.3*0.4    0.12
P(h2|Y=0) =   --------------  = ------- = ------
                  P(Y=0)         P(Y=0)   P(Y=0)

So the h2 is the more probable hypothesis, as P(Y=0)>0