Ensemble-based inference of multi-dimensional Hawkes process driven by count data

The vision of this research is to develop a novel sequential inference method for constructing a large-scale influence network from spatio-temporal count data, which could encompass an arbitrary number of events in a time interval, both as a batch and real-time data stream. The main outcome will a provide a statistical tool to assimilate sequences of count data observed from multiple sources to construct a directed network whose links represent the influence among the data sources. In particular, the influence network will be parameterised by a multi-dimensional Hawkes process driven by count data, which is a stochastic process of the conditional intensity of a count-data process. The ensemble-based idea is adopted to enable the uncertainty analysis of the inferred network structure via ensemble spread. Understanding uncertainty is crucial in trying to reach a sensible conclusion in a complicated situation where multiple network structures should be considered. The outcome of this work will also facilitate downstream uncertainty analysis for network applications such as node classifications, link prediction and rare-event detection. The ensemble-based approach here has a similar idea to the well-known ensemble Kalman filter (EnKF), which is instrumental to sequential data assimilation problems in geophysical and dynamical system applications. This framework can be efficient in constructing a large-scale influence network due to its highly parallisable scheme under somewhat general assumption of conditional independence of the data.

The ideal candidates will have a strong background in some of the following areas: mathematical statistics, inverse problems, machine learning, optimisation and/or numerical analysis. Experience in programming (e.g. MATLAB, Python and/or R) is highly desirable.

The successful candidate will receive comprehensive research training related to all aspects of the research and opportunities to participate in conferences, workshops and seminars to develop professional skills and research network.

Supervisors: Dr Naratip Santitissadeekorn and Professor David Lloyd.

This is a minimum 3 year project. We are able to offer this opportunity starting in October 2022.

Entry requirements

Applicants should have a minimum of a first class honours degree in mathematics, the physical sciences or engineering. Preferably applicants will hold a MMath, MPhys or MSc degree, though exceptional BSc students will be considered.

English language requirements: IELTS Academic 6.5 or above (or equivalent) with 6.0 in each individual category.

How to apply

Applications should be submitted via the Mathematics PhD programme page on the "Apply" tab.

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