CASE Studentship
'Multiscale Methods In Spatial Inference'
University of Warwick
The four-year studentship provides the opportunity for research, towards a PhD in Mathematics, on the analysis of statistical inference problems in the context of spatial tracking. The research is motivated by the problem of identifying large numbers of moving sources of radio emissions and will be undertaken in collaboration with SELEX Galileo Ltd.
Expressing the tracking problem in the framework of Bayesian statistical inference it is immediately apparent that the resulting optimisation problem will be far from convex. The posterior probability will have many local maxima and the research will pursue complexity reduction by using appropriate filters defining a hierarchy of sub-problems at different scales to enable an efficient numerical solution. This research will provide the opportunity for applying developed methods to communication-band data with SELEX-Galileo Ltd.
Students with a more theoretical inclination would be invited to investigate closely related mathematical problems which are motivated by the multiscale structure of the data. High dimensional optimization problems with many local extrema can be studied with powerful tools from variational calculus, such as Γ-convergence. A systematic application of multiscale methods to Bayesian Statistics can provide a rigorous mathematical derivation of coarse grained variables that represent the most important information content of the data. A systematic exploration of this approach would be highly desirable and pave the way for treating many important related problems.
Ideal applicants for the studentship have completed a 4-year Mathematics education with a first class degree.
Enquiries: Florian Theil, Mathematics Institute, Warwick University, f.theil@warwick.ac.uk.
