Solutions - Bayesian Networks in R: With Applications in Systems Biology - page 142

The conditional probability of the two events is not equal to the product of the
corresponding marginal probabilities; therefore, STAT and MECH are not inde-
pendent given the evidence on ALG . Note that the fact that ALG d-separates STAT
and MECH is not relevant in this case, because the evidence on ALG is soft evi-
dence (i.e., ALG is still a random variable, just with a different distribution).
(c) > cpquery(fitted,
+ event = ((MECH >= 60) & (MECH <= 70)) |
+ ((VECT >= 60) & (VECT <= 70)),
+ evidence = (ALG >= 90), n = 5 * 10ˆ6)
4.4 Using the dynamic Bayesian network dbn2 from Sect. 4.3 , investigate the
effects of genes 257710 at and 255070 at observed at time t − 2 on gene

265768 at at time t .

> cpquery(dbn2.fit, event = ('265768_at' > 8),
+ evidence = ('257710_at' > 8))

[1] 0.3571429
> cpquery(dbn2.fit, event = ('265768_at' > 8),
+

evidence = ('255070_at' > 8))

[1] 0.5903756
> cpquery(dbn2.fit, event = ('265768_at' > 8),
+

evidence = TRUE)

[1] 0.4427231
High expression levels of gene 257710 at at time t 2 reduce the probability of

high expression levels of gene 265768 at at time t ; the opposite is true for gene
255070 at .

−

Exercises of Chap. 5

5.1 Using the hailfinder data set included in bnlearn and a snow cluster
with at least 2 slave processes:

(a) Compute the number of levels and the most common level for each node.
(b) Split the samples among the slaves, and identify which nodes have at least
one level with less than 5 observations in that particular subsample.
(c) Compute the entropy of each variable in hailfinder , defined as

)= ∑ − p log p H ( p

where p is the relative frequency of each level of the variable.

(a) > library(bnlearn)
> library(snow)
> clusterSetupSPRNG(cl)
> cl = makeCluster(2, type = "SOCK")