Bayesian Network Inference Algorithms - Bayesian Networks in R: With Applications in Systems Biology - page 90

4.2 Inference in Static Bayesian Networks
Consider again the protein-signaling network and the data set from Sachs et al.
( 2005 ) we analyzed in Sect. 2.5 .
> isachs = read.table("sachs.interventional.txt",
+ header = TRUE, colClasses = "factor")
Before we can use either bnlearn or gRain to apply the approaches illustrated in
Sect. 4.1 , we need to create a bn object for the validated network structure from
Sachs et al. ( 2005 ) and perform parameter learning.
> library(gRain)
> library(bnlearn)
> val.str = 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.str)
> isachs = isachs[, 1:11]
> for (i in names(isachs))
+ levels(isachs[, i]) = c("LOW", "AVG", "HIGH")
> fitted = bn.fit(val, isachs, method = "bayes")
The INT variable, which codifies the intervention applied to each observation, is
not needed for inference and is therefore dropped from the data set. Furthermore,
we rename the expression levels of each protein to make both the subsequent R code
and its output more readable.
The reason for setting method to "bayes" in bn.fit is twofold. First,
Bayesian estimates for the parameters of the network are smoother than the maxi-
mum likelihood ones, making inference both easier and more robust. Furthermore,
Koller and Friedman ( 2009 ) showed that such estimates produce Bayesian networks
that are close to the “true” networks for small imaginary sample sizes. On a related
note, using Bayesian parameter estimates also guarantees that conditional proba-
bility tables are always completely specified (i.e., without missing values) even for
small data sets.
4.2.1 Exact Inference
In their paper, Sachs et al. ( 2005 ) performed two conditional probability queries
using the validated Bayesian network val :
1. A direct perturbation of p44.42 should influence pakts473 .
2. A direct perturbation of p44.42 should not influence PKA .