Inference in Bayesian Networks

How can one infer the (probabilities of) values of one or more network variables, given observed values of others?
Bayes net contains all information needed for this inference.
If there is only one variable with an unknown value then easy to infer it.
In the general case theproblem is NP hard.
In practice, we can succeed in many cases:
Exact inference methods work well for some network structures.
Monte Carlo methods “simulate” the network randomly to calculate approximate solutions.