Solutions - Bayesian Networks in R: With Applications in Systems Biology - page 141

> querygrain(jtree, nodes = query)
> querygrain(jprop, nodes = query)
> jprop = setFinding(jtree, nodes = "PKA",
+ states = "HIGH")
> querygrain(jtree, nodes = query)
> querygrain(jprop, nodes = query)

When PKA is HIGH , the activity of all the proteins corresponding to the query
nodes is inhibited (the LOW probability increases and the HIGH decreases).
When PKA is LOW , the opposite is true (the LOW probability decreases and the
HIGH increases).
(c) Continuing from the previous two points,

> jprop = setFinding(jtree,
+ nodes = c("PIP2", "PIP3", "plcg"),
+ states = rep("LOW", 3))
> a = querygrain(jtree, nodes = "pjnk")
> b = querygrain(jprop, nodes = "pjnk")
> identical(a, b)
Ourbeliefonthe pjnk node is completely unaffected by any evidence on either
PIP2 , PIP3 ,or plcg , because there is no path from the former to the any of
the latter. Therefore, changes in belief due to new evidence cannot propagate
from PIP2 , PIP3 ,and plcg to pjnk .

4.3 Consider the marks data set analyzed in Sect. 2.3 .
(a) Learn both the network structure and the parameters with likelihood-
based approaches, i.e., BIC or AIC, for structure learning and maximum
likelihood estimates for the parameters.
(b) Query the network learned in the previous point for the probability to have
the marks for both STAT and MECH above 60 , given evidence that the mark
for ALG is at most 60 . Are the two variables independent given the evidence
on ALG ?
(c) What is the (conditional) probability of having an average vote (in the
[

range) in both VECT and MECH while having an outstanding vote
in ALG (at least 90 )?

60 , 70 ]

(a) > bn = hc(marks, score = "bic-g")
> fitted = bn.fit(bn, marks)
(b) > cpquery(fitted,
+ event = (STAT > 60) & (MECH > 60),
+ evidence = (ALG <= 60), n = 5 * 10ˆ6)
> cpquery(fitted, event = (STAT > 60),
+ evidence = (ALG <= 60), n = 5 * 10ˆ6)
> cpquery(fitted, event = (MECH > 60),
+ evidence = (ALG <= 60), n = 5 * 10ˆ6)