Learning Bayesian Networks from Ordinal Data - The Bayesian Way

We propose a new Bayesian method for Bayesian network structure learning from ordinal data. Our Bayesian method is similar to a recently proposed non-Bayesian method, referred to as the ordinal structural expectation maximization (OSEM) method. Both methods assume that the ordinal variables originate from Gaussian variables, which can only be observed in discretized form, and that the dependencies in the unobserved latent Gaussian space can be described in terms of Gaussian Bayesian networks. In our simulation studies the new Bayesian method yields significantly higher network reconstruction accuracies than the OSEM method.