Statistical Learning:

In the example presented in the class taken from the textbook there were 5 kinds of bags of candies:

10% were h₁: 100% cherry candies

20% were h₂: 75% cherry candies + 25% lime candies

40% were h₃: 50% cherry candies + 50% lime candies

20% were h₄: 25% cherry candies + 75% lime candies

10% were h₅: 100% lime candies

Then 10 candies were drawn one after another from some unknown bag all of them turned out to be lime candies. The picture below shows the result of computation of hypotheses pending observed data

P(h_i | d) = P(d | h_i) P(h_i ), i=1,2,,5, = 1 / P(d ) is the normalization constant needed to make the entries in P(h_i | d) to sum to 1. Derive the results P(h_i | d), i=1,2,,5, for 0,1,2,,10 samples in d and verify whether they are the same as in the picture below.

Posterior probability of hypotheses P(h, I d) P(h 0.8 I d) o 0.6 0.4 0.2 10 Number of samples in d Chapter 20, Sections 1-3 5