You can use the variable elimination algorithm (pushing sums inside
products) to compute a marginal on any *single* set of nodes in one pass
over the network. (Choosing an optimal summation ordering is NP-hard.)
% For details, see
% - R. Dechter, "Bucket Elimination: A Unifying Framework for
Probabilistic Inference", UA1 96, pp. 211-219.
% - Z. Li and B. D'Ambrosio, "Efficient inference in Bayes networks as a
combinatorial
% optimization problem", Intl. J. Approximate Reasoning,
11(1):55-81, 1994
% - R. McEliece and S. M. Aji, "The Generalized Distributive Law", IEEE
Trans. Inform. Theory, to appear
HTH,
Kevin
