frozenca / ml-murphy

Complete solutions for exercises and MATLAB example codes for "Machine Learning: A Probabilistic Perspective" 1/e by K. Murphy

ML-Murphy

Complete solutions for exercises and MATLAB example codes for "Machine Learning: A Probabilistic Perspective" 1/e by K. Murphy

ml-murphy's Issues

Solution to 3.18 doesn't seem right

I just worked out question 3.18 myself, and found an answer of 9.31. Which differs by one decimal position from the answer in this repo.

I found this other solution manual here that like me also arrived a 9.31:
https://github.com/ArthurZC23/Machine-Learning-A-Probabilistic-Perspective-Solutions/blob/master/3/18.pdf

I think the mistake here is in the step where the uniform pmf gets plugged in, resulting in a P(D | M_1) = 1/(N+1).
Assuming that M_1 here refers to the alternative hypothesis H1, this doesn't seem right.

This seems like it should be:

P(D | H_1) = \int_{0}^{1} L(\theta | D) P(\theta | H_1)

With L(\theta | D) the likelihood function and P(\theta | H_1) the uniform prior on \theta as specified in the alternative hypothesis.

Calculating that integral, we find a denominator of 110 rather than 11.

In the numerator, strictly speaking this integral exists there too:
P(D | H_0) = \int_{0}^{1} L(\theta | D) P(\theta | H_0)

However, in the numerator that doesn't matter because P(\theta | H_0) has a Dirac point mass on 0.5, and thus the integral drops off and we are left with only the Bernoulli likelihood function.

Typo in solution 5.1

In your solution 5.1 line 5,
I guess the denominator should be p(D | z=k), instead of p(\theta | z=k)

What does /mu mean here?