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Graphical models or networks describe the statistical dependence amongmultiple variables and are widely used in biology (e.g., gene regulatorynetworks). Under appropriate assumptions, directed edges may represent causalrelationships. A key feature of a biological network is sparsity, defined byhow likely an edge is present, of which we often have some knowledge. However,most existing Bayesian methods use priors for the entire graph, making itdifficult to specify the level of sparsity. The few methods that use priors onedges estimate the two directions independently; the sum of the twoprobabilities can exceed 1. Here, we present baycn (BAYesian Causal Network), anovel approximate Bayesian method that represents a graph in terms of threestates of edges: the two directions and edge absence, and specifies priors onthese edge states. We design a pseudo Bayesian sampling algorithm for efficientinference. We apply baycn to two genomic problems: i) distinguishing direct andindirect target genes of genetic variants, using these variants as instrumentalvariables, and ii) inferring combinatorial binding of highly-correlatedtranscription factors in Drosophila. In both cases and in extensivesimulations, our method demonstrates much improved accuracy over existingmethods for the whole graph and for individual edges.

Approximate Bayesian inference of directed acyclic graphs in biology with flexible priors on edge states