Stochastic Prediction for the Design and Management of Interacting Complex Systems

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This research considers systems that combine social networks and sensor networks with complicated interactions involving hierarchical structure. To design and analyze such complex distributed systems, information-theoretical methods will be combined with advanced Bayesian and non-Bayesian statistical techniques such as spatiotemporal nonlinear estimation and prediction, advanced changepoint detection and estimation methods, and multihypothesis decision-making strategies. Advanced data fusion methods at different levels will be proposed and tested. Distributed networks will be modeled by quite general coupled fractional hidden Markov models adapted to allow for nonlinear prediction and detection-classification. The spaces in which estimation, prediction, and classification are performed may be both metric and symbolic, thus allowing for the effective incorporation of sensor (metric) and social (symbolic) networks as a part of a large-scale distributed system. Design of complex multi-level hierarchical systems, including systems that search for patterns to identify developing or immediate threats, is vitally important for various areas, including national security, environmental monitoring, SmartGrid and other critical infrastructures. This research will develop novel approaches for automated efficient fusion of information from multiple sources or/and from multiple levels of hierarchy of complex systems that will enable these systems to achieve high accuracy in detection of changes in trends, prediction, and recognition. Probabilistic modeling of networks will be coupled with novel approaches to event pattern recognition, change detection and information integration/fusion in complex, multisource-multisensor distributed heterogeneous systems. Both mathematical formulations and solution algorithms will be developed.