Comparing Dependent Undirected Gaussian Networks

Abstract

A Bayesian approach is proposed, which unifies network constructions and comparisons between two longitudinal undirected Gaussian networks on their differentiation status (identical or differential) for data collected at two time points. Utilizing the concept of modeling repeated measures, we construct a joint likelihood of networks. The conditional posterior probability mass function for network differentiation is derived and its asymptotic proposition is theoretically assessed. An alternative approach built upon latent rather than manifest data is proposed to significantly reduce computing burden. Simulations are used to demonstrate and compare the two methods and compare them with existing approaches. Based on epigenetic data collected at different ages, the proposed methods are demonstrated on their ability to detect dependent network differentiations. Our theoretical assessment, simulations, and real data applications support the effectiveness of the proposed methods, although the approach relying on latent data is less efficient.