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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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