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We study the problem of learning Bayesian network structures from data.Koivisto and Sood (2004) and Koivisto (2006) presented algorithms that cancompute the exact marginal posterior probability of a subnetwork, e.g., asingle edge, in O(n2n) time and the posterior probabilities for all n(n-1)potential edges in O(n2n) total time, assuming that the number of parents pernode or the indegree is bounded by a constant. One main drawback of theiralgorithms is the requirement of a special structure prior that is non uniformand does not respect Markov equivalence. In this paper, we develop an algorithmthat can compute the exact posterior probability of a subnetwork in O(3n) timeand the posterior probabilities for all n(n-1) potential edges in O(n3n) totaltime. Our algorithm also assumes a bounded indegree but allows generalstructure priors. We demonstrate the applicability of the algorithm on severaldata sets with up to 20 variables.

Computing Posterior Probabilities of Structural Features in Bayesian Networks