A Bayesian Approach to Directed Acyclic Graphs with a Candidate Graph
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Directed acyclic graphs represent the dependence structure among multiple variables. When learning these graphs from data, different amounts of information may be available for different edges. Although many methods have been developed to learn the topology of these graphs, most of these methods do not provide a measure of the uncertainty in the inference. Here, we propose a Bayesian method, namely baycn (BAYesian Causal Network), to estimate the posterior probability of three states for each inferred edge: present with one direction (X → Y), present with the opposite direction (X ← Y), and absent. Unlike existing Bayesian methods, our method requires that the prior probabilities of the three states be specified, and therefore provides a coherent interpretation of the posterior probabilities. We develop a fast Metropolis-Hastings Markov chain Monte Carlo algorithm for the inference. To perform the inference efficiently, our algorithm takes as input a candidate graph, which may be the output of another graph inference method and may contain false edges. In simulation studies our method achieves high accuracy with small variation across different scenarios and is comparable or better than existing Bayesian methods.
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