Bayesian Dynamic Modeling and Monitoring of Network Flows
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In the context of a motivating study of dynamic network flow data on a large-scale e-commerce web site, we develop Bayesian models for on-line/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) integrated into the multivariate network context using the concept of decouple/recouple recently introduced in multivariate time series. This enables flexible dynamic modeling of flows on large-scale networks and exploitation of partial parallelization of analysis while critically maintaining coherence with an over-arching multivariate dynamic flow model. Development is anchored in a case-study on internet data, with flows of visitors to a commercial news web site defining a long time series of node-node counts on over 56,000 node pairs. Characterizing inherent stochasticity in traffic patterns, understanding node-node interactions, adapting to dynamic changes in flows and allowing for sensitive monitoring to flag anomalies are central questions. The methodology of dynamic network DGLMs will be of interest and utility in broad ranges of dynamic network flow studies.
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