An excellent introduction to Bayesian reasoning (the proponents of which have replaced the Illuminati as the secret rulers of the world) can be found here.
And there's a good tutorial on Bayesian Networks here, with respect to a Bayesian net computer utility. Surprisingly, I understood a lot of it; partly because I have done some (very minor) stuff using directed acyclic graphs. (They are coming to be used somewhat in philosophy of causation, because they are very handy for representing relations of dependence.)
(Hat-tip to Franz Dill at Future Now.)