Bayesian Networks in the Absence of Temporal Information - Bayesian Networks in R: With Applications in Systems Biology - page 42

+ "ALG" = 1), sd = 10)
> ALG.par = list(coef = c("(Intercept)" = 25,
+ "ANL" = 0.5, "STAT" = 0.25), sd = 6.5)
> ANL.par = list(coef = c("(Intercept)" = 25,
+ "STAT" = 0.5), sd = 12)
> STAT.par = list(coef = c("(Intercept)" = 43),
+ sd = 17)
> dist = list(MECH = MECH.par, VECT = VECT.par,
+ ALG = ALG.par, ANL = ANL.par,
+ STAT = STAT.par)
> fitted2 = custom.fit(bn.gs, dist = dist)
Note that the network structure stored in the object of class bn passed to bn.fit
and custom.fit must be a DAG; any undirected arc must be either dropped (with
the drop.arc function) or replaced with a directed one (with the set.arc func-
tion). As an alternative, if the network structure is a completed partially acyclic
graph representing an equivalence class, we can also use the cextend function to
consistently extend it to a DAG ( Dor and Tarsi , 1992 ).

2.3.6 Discretization

We consider now how to discretize the marks data set while at the same time pre-
serving the dependence structure of the data and how this transformation changes
the results of Bayesian network learning. For instance, we can discretize each vari-
able in the marks data into a dichotomic one by a median split transform (so that
students with marks above the median are in one category and students below the
median are in the other one). If we learn the network structure of this new data set,
using the Grow-Shrink and hill-climbing algorithms as we did in Sect. 2.3.4 ,weget
the networks shown in Fig. 2.6 .

> dmarks = discretize(marks, breaks = 2,
+ method = "interval")

> bn.dgs = gs(dmarks)
> bn.dhc = hc(dmarks)
> all.equal(cpdag(bn.dgs), cpdag(bn.dhc))
[1] TRUE
Both networks belong again to the same equivalence class, and we can see that
part of the dependence structure of the original network is still present: ALG still
d-separates ANL and STAT from MECH and VECT , but the arc between ANL and
STAT and the one between ALG and MECH are missing.
Since all the variables are now discrete, the parameters of the Bayesian net-
work are the elements of the CPTs, as discussed in Sect. 2.2.4 . For example, for
the bn.dhc network, they can be learned and displayed as follows: