Bayesian Network Inference Algorithms - Bayesian Networks in R: With Applications in Systems Biology - page 91

The resulting posterior distributions were then compared with the results of two
ad hoc experiments to confirm the validity and the direction of the inferred causal
influences.
Given the size of the network, we can perform both queries using any of the
exact and approximate inference algorithms introduced in Sect. 4.1.2 . First, we will
start with the implementation of the junction tree algorithm provided by the gRain
package.
> jtree = compile(as.grain(fitted))
The compile function performs all the steps shown in Algorithm 4.1 and takes the
grain object returned by as.grain as an argument. The latter function, along
with as.bn.fit , provides an easy way to export Bayesian networks from bnlearn
to gRain and vice versa, thus integrating the functionality of these two packages.
We can then introduce the direct perturbation of p44.42 required by both
queries by calling setFinding as follows (Fig. 4.1 ). In causal terms, this would
be an ideal intervention.
> jprop = setFinding(jtree, nodes = "p44.42",
+ states = "LOW")
As we can see from the code below, the marginal distribution of pakts473 is
similar whether or not we take the evidence (intervention) into account.
> querygrain(jtree, nodes = "pakts473")$pakts473
pakts473
LOW AVG HIGH
0.60893407 0.31041282 0.08065311
> querygrain(jprop, nodes = "pakts473")$pakts473
pakts473
LOW AVG HIGH
0.665161776 0.333333333 0.001504891
The slight inhibition of packts473 resulting from the inhibition of p44.42
agrees with both the direction of the arc linking the two nodes and the additional
experiments performed by Sachs et al. ( 2005 ). In causal terms, the fact that changes
in p44.42 affect packts473 supports the existence of a causal link from the
former to the latter.
As far as PKA is concerned, both the validated network and the additional ex-
perimental evidence support the existence of a causal link from PKA to p44.42 .
Therefore, interventions to p44.42 cannot affect PKA . However, knowledge of the
expression level of p44.42 may still alter our expectations on PKA if we treat it as
evidence instead of an ideal intervention.
> querygrain(jtree, nodes = "PKA")$PKA
PKA
LOW AVG HIGH
0.1943315 0.6956254 0.1100431