  Probabilistic inference in graphical models is the task of computing marginal
and conditional densities of interest from a factorized representation of a
joint probability distribution. Inference algorithms such as variable
elimination and belief propagation take advantage of constraints embedded in
this factorization to compute such densities efficiently. In this paper, we
propose an algorithm which computes interventional distributions in latent
variable causal models represented by acyclic directed mixed graphs(ADMGs). To
compute these distributions efficiently, we take advantage of a recursive
factorization which generalizes the usual Markov factorization for DAGs and the
more recent factorization for ADMGs. Our algorithm can be viewed as a
generalization of variable elimination to the mixed graph case. We show our
algorithm is exponential in the mixed graph generalization of treewidth.
