#### Nihat Ay, Philip Moritz, Jörg Reichardt

Paper #: 13-03-010

Given an observed subset Y1 , . . . , Yk of variables in a fixed Bayesian network G, our main result is a tight bound on the generalized mutual information Ic(Y1,...,Yk) = ∑ j =1kH(Yj)/c − H(Y1, . . . ,Yk) over all probability distributions satisfying G. Our bound depends on the ancestral structure of the nodes in the network. It makes it possible to discriminate between different causal models for a probability distribution, as we show from numerical experiments.