Q$3)$ The "carcass" data from the package "gRbase" contains data on meat. Specifically, the data

describes the thickness of meat and fat layers in different regions on the back of a pig together

with the lean meat percentage on each of $344$ carcasses. The data has been used for the prediction

of lean meat percentage based on carcass thickness.

a$)$ Create a BN using score$-$based structural learning and ensure that "Lean Meat" is at the

bottom of the network.

b$)$ Create a BN using conditional independence tests for structural learning and ensure that

"Lean Meat" is at the bottom of the network.

c$)$ How do the networks in A$-$B compare?

d$)$ Simulate a dataset from your BN in part A with $25$ samples, then learn the structure, how

does the model compare with A$?$

e$)$ Simulate a dataset from your BN in part A with $100$ samples, then learn the structure, how

does the model compare with $A?$

f$)$ How does sample size impact structural and parameter learning?