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> cpd =
+ cpdist(dbn2.fit, node = "245094_at", evidence =
+ ('245094_at1' > 6.5) & ('245094_at1' < 7.5) &
+ ('265768_at' > 7) & ('265768_at' < 8))
> summary(cpd)
245094_at
Min. :7.874
1st Qu.:8.209
Median :8.419
Mean :8.428
3rd Qu.:8.612
Max. :9.046
If the expression level of
245094 at
at time
t
1 has been observed, we are
smoothing it; if it were missing, we would be imputing it with the mean of its con-
ditional distribution (8
−
.
428), that is, its most probable explanation.
Exercises
4.1.
Apply the junction tree algorithm to the validated network structure from
Sachs
et al.
(
2005
), and draw the resulting undirected triangulated graph.
4.2.
Consider the
Sachs et al.
(
2005
) data used in Sect.
4.2
.
(a) Perform parameter learning with the
bn.fit
function from
bnlearn
and the
validated network structure. How do the maximum likelihood estimates differ
from the Bayesian ones, and how do the latter vary as the imaginary sample size
increases?
(b) Node
PKA
is parent of all the nodes in the
praf
→
pmek
→
p44.42
→
pakts473
chain. Use the junction tree algorithm to explore how our beliefs
on those nodes change when we have evidence that
PKA
is “
LOW
,” and when
PKA
is “
HIGH
.”
(c) Similarly, explore the effects on
pjnk
of evidence on
PIP2
,
PIP3
,and
plcg
.
4.3.
Consider the
marks
data set analyzed in Sect.
2.3
.
(a) Learn both the network structure and the parameters with likelihood-based ap-
proaches, i.e., BIC or AIC, for structure learning and maximum likelihood esti-
mates 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
?
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