Exercise 2 [ 30%] Consider the following graphs with 4 vertices: G1 = {(1, 2); (1, 4); (2, 3)} G2 = {(1, 3); (2, 3); (3, 4); (1, 4); (2, 4)} G3 = {(2, 4),(2, 3)} G4 = {(1, 2); (3, 4); (2, 3); (2, 4)} G5 = {(2, 3); (2, 4); (3, 4)}. The above notation means: if a pair (i, j) is present in the graph then there is an edge between i and j. We adopt a Bayesian approach and we assume that the data follows a 4- dimensional Gaussian distribution. Infer the graph structure (and motivate your answer) when the posterior probabilities for the graphs are: 1 1. (G1|data) = 0.2, (G2|data) = 0.5, (G3|data) = 0.1, (G4|data) = 0.1 and (G5|data) = 0.1. [10 marks] 2. (G1|data) = 0.08, (G2|data) = 0.23, (G3|data) = 0.23, (G4|data) = 0.23 and (G5|data) = 0.23. [10 marks] 3. (G1|data) = 0.3, (G2|data) = 0.08, (G3|data) = 0.3, (G4|data) = 0.02 and (G5|data) = 0.3. [10 marks]