Bayesian dynamic modeling and monitoring of network flows

In the context of a motivating study of dynamic network flow data on a large-scale e-commerce website, we develop Bayesian models for online/sequential analysis for monitoring and adapting to changes reflected in node–node traffic. For large-scale networks, we customize core Bayesian time series analysis methods using dynamic generalized linear models (DGLMs). These are integrated into the context of multivariate networks using the concept of decouple/recouple that was recently introduced in multivariate time series. This method enables flexible dynamic modeling of flows on large-scale networks and exploitation of partial parallelization of analysis while maintaining coherence with an over-arching multivariate dynamic flow model. This approach is anchored in a case study on Internet data, with flows of visitors to a commercial news website defining a long time series of node–node counts on over 56,000 node pairs. Central questions include characterizing inherent stochasticity in traffic patterns, understanding node–node interactions, adapting to dynamic changes in flows and allowing for sensitive monitoring to flag anomalies. The methodology of dynamic network DGLMs applies to many dynamic network flow studies.