Homework 10

For the data in the example on page 87 of the notes, we settled on a possible model corresponding to a distribution that factors as $p(x_1,x_2,x_3) = p(x_1)p(x_2 | x_1)p(x_3 | x_2)$.  

a) Find a undirected graph $G$ such that the discrete DAG model $\mathcal{M}(G)$ is all discrete distributions having such a factorization. 

b) Decide if $\mathcal{M}(G)$ is a good fit for the data-generating distribution based on the data on page 87 of the notes. Be sure to justify your decision with an (approximate) p-value.