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

Graphical models are widely used to represent dependence structures in biological systems, where directed edges may encode causal relationships under appropriate assumptions. We present baycn (BAYesian Causal Network), a novel approximate Bayesian method for inferring probabilities of edge directions and edge absence, while allowing flexible, user-specified priors to encode sparsity and an input graph to incorporate biological knowledge. For inference, we develop a Metropolis-Hastings-like sampler over graph structures based on a pseudo-posterior with a plug-in likelihood, which eliminates potentially high-dimensional nuisance parameters. This formulation substantially improves computational efficiency while yielding posterior probabilities that reflect Markov equivalence. We apply baycn to two genomic applications: distinguishing direct from indirect target genes of a shared genetic variant, and inferring combinatorial binding of transcription factors during tissue differentiation in Drosophila embryos. Both applications involve discrete and continuous data types that are common in genomics. Selected variables in these applications are treated as instrumental variables to help impose constraints on edge direction. Baycn demonstrates substantially improved accuracy at both the graph and edge levels, while existing methods do not handle mixed data, fail to capture weak signals, or are computationally infeasible.Author summary: Biological networks are widely used to describe relationships among genes, proteins, and other molecular features, but inferring which connections are real and which way information flows remains challenging. We present baycn, a Bayesian method that assigns probabilities to three possible states for each potential connection: A to B, B to A, or no edge. This edge-based representation allows researchers to incorporate prior biological knowledge, such as expected sparsity or known constraints. Baycn is designed to be computationally efficient, making it practical for real genomic studies. The estimated edge-state probabilities are well calibrated. It can analyze data that include both discrete and continuous values, which are common in genomics, and can use selected variables to improve inference of edge direction. Across simulations and two genomic applications, baycn achieves higher accuracy than existing approaches.