
52 Bayesian Networks: With Examples in R
2.5.2 Network Scores
Network scores for GBNs have much in common with the scores for discrete
BNs we introduced in Section 1.5.2. For instance, BIC takes the form
BIC = log
b
f(E, G, V, N, W, C) −
d
2
log n =
=
log
b
f(E) −
d
E
2
log n
+
log
b
f(G) −
d
G
2
log n
+
+
log
b
f(V | E, G) −
d
V
2
log n
+
log
b
f(N | V) −
d
N
2
log n
+
+
log
b
f(W | V) −
d
W
2
log n
+
log
b
f(C | N, W) −
d
C
2
log n
(2.13)
where each local distribution is normally distributed with the parameters we
estimated in Section 2.4. So, for instance,
b
f(C | N, W) = N(bµ
C
+ N
b
β
N
+ W
b
β
W
, bσ
2
C
) (2.14)
where bµ
C
= 0,
b
β
N
= 0.3221,
b
β
W
= 0.6737 and the residual variance bσ
2
C
= 5.8983.
Likewise,