Locally Adaptive Dynamic Networks

Our focus is on realistically modeling and forecasting dynamic networks of face-to-face contacts among individuals. Important aspects of such data that lead to problems with current methods include the tendency to move between periods of slow and rapid changes and the dynamic heterogeneity in the connectivity behaviors across nodes. Motivated by this application, we develop a novel methodology for Locally Adaptive DYnamic (LADY) network inference. The proposed model relies on a dynamic latent space representation in which each subjects' position evolves over time via a stochastic differential equation. Using a state space representation for these stochastic processes and P\'olya-gamma data augmentation, we develop an efficient MCMC algorithm for posterior inference along with tractable online updating and prediction procedures for forecasting of future networks. We evaluate performance via simulation studies, and consider an application to face-to-face contacts among students in a primary school.