Ensemble-based filtering for uncovering an influence network from Hawkes processes driven by count data

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Many networks such as communication, social media, covert and criminal networks have event-driven dynamics where the intensity rate of the events is changed according to the historical number of events in the network. In particular, events generated by a node of the network may increase or decrease the intensity of other nodes depending on their causal relationship. Such a network structure is called a causal or influence network of which the links represent the directional influence between nodes. The proposed research offers the prospect of a sequential data assimilation tool for inference of influence network from a time-series of count data. The outcome will provide an insight into the complex interaction in which events generated by a node in the network could change the intensity rate of other nodes.For example, in the context of crime hot spots, crime occurrences in some spatial locations could increase the crime rate in others through complex reactions of criminals in each area over crime events. Linkages between crime occurrences in spatial locations can be represented as a complex network where each link is weighted by the strength of the influence of crime events from one location to another. The structure of the influence network will inform rationale strategies for proactive policing. The research outcome can also be used in other similar application contexts (e.g. opinion networks in social science, earthquake networks, terrorist networks, or healthcare networks) where complex influence structure is of interest.