In this subsection we recast the robust inference problem as a parameter estimation problem. Consider a transformed Bayesian network with transparent variables z'i. Each transparent variable has values 1, 2, ..., |z'i|;. Suppose z'i is a random variable with distribution thetaij = p(z'i = j). Call Theta the vector of all thetaij.
Suppose xq is queried; the objective is to find:
Notice that the optimization procedure has to be repeated for each of the
values of the queried variable.
To solve the robust inference problem, we must maximize the posterior log-likelihood for Theta:
Fri May 30 15:55:18 EDT 1997