=+13.24. Consider Example 13.4.

(i) Recall that the best model in terms of BP is the one that maximizes C1(M), defined below (13.95). Show that C1(M) =

⎧

⎨

⎩

(49/640)a2m, M = M1 0, M = M2

(49/640)a2m, M = M3.

Thus, the best model under BP is M1, because it has the same (maximum)

C1(M) as M3 but is simpler.

(ii) Recall the best model under GIC is the one that minimizes C2(M), defined below (13.93). Show that C2(M) =

⎧

⎨

⎩

s + λm − 1, M = M1, s + λm − 1 − (49/712)a2m, M = M2, s + 2(λm − 1)1 − (49/712)a2m, M = M3, where s = m i=1(A + Di)−1μ2 i . Thus, M2 is the best model under the GIC.