Solutions - Bayesian Networks in R: With Applications in Systems Biology - page 140

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 be-
liefs 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 .

(a) Parameter fitting can be carried out as follows:

> library(bnlearn)
> val.spec = paste("[PKC][PKA|PKC][praf|PKC:PKA]",
+ "[pmek|PKC:PKA:praf][p44.42|pmek:PKA]",
+ "[pakts473|p44.42:PKA][P38|PKC:PKA]",
+ "[pjnk|PKC:PKA][plcg][PIP3|plcg]",
+ "[PIP2|plcg:PIP3]")
> val = model2network(val.spec)
> isachs = isachs[, 1:11]
> for (i in names(isachs))
+ levels(isachs[, i]) = c("LOW", "AVG", "HIGH")
> fitted = bn.fit(val, isachs, method = "mle")
> fitted2 = bn.fit(val, isachs, method = "bayes",
+ iss = 5)
> fitted3 = bn.fit(val, isachs, method = "bayes",
+ iss = 10)
> fitted4 = bn.fit(val, isachs, method = "bayes",
+

iss = 20)

The main difference between maximum likelihood and Bayesian estimates is
that the former can contain NaN s, while the latter are always completely spec-
ified. This happens when, for a particular node, some of the parents' configu-
rations are not observed; therefore, the distribution of the node conditional on
that configuration cannot be estimated from the data. In Bayesian estimates,
such unknown conditional distributions result in the posterior being equal to
the prior, that is, uniform.
As for the effects of the imaginary sample size, larger values result in smoother
estimates because of the increasing weight given to the uniform prior compared
to the sample. Posterior parameter estimates move away from 0 and 1, and there-
fore inference is affected by fewer numerical problems.
(b) Continuing from the previous point,

> library(gRain)
> jtree = compile(as.grain(fitted))
> jprop = setFinding(jtree, nodes = "PKA",
+ states = "LOW")
> query = c("praf", "pmek", "p44.42", "pakts473")