The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2016 (funded students) or at any point in the academic year (self-funded students).
Particle filters are a class of recursive Monte Carlo methods for estimation, tracking and prediction in stochastic dynamical systems. They have become hugely popular in the last 15 years because of their many applications in engineering, finance, biochemistry, ecology and other fields. One important problem when tackling a practical problem using a particle filter is how to set the ‘computational budget’ of the algorithm: as other Monte Carlo methods, particle filters rely on the generation of collections of random samples and it is often far from straightforward to determine how large this collection should be in order to attain a prescribed accuracy in the tracking or prediction tasks. While one can think of generating a very large number of random samples to guarantee a good performance, this comes at the expense of an increased computational cost, which may not be met in many applications (for example, if data are received and have to be processed by the filter very frequently).
Therefore, there is a need for reliable methods to assess the performance of particle filters in real time (e.g., to check whether the prediction error for some variable of interest has converged to a sufficiently small value) without siginificantly increasing the complexity of the algorithm. In this project, we will start from preliminary results on the approximation of predictive distributions for state-space models and aim at extending them into rigorous procedures to (a) assess the convergence of the most widely-used classes of particle filters and (b) propose new algorithms that exploit the ability to evaluate convergence in order to automatically adjust the computational effort. Besides a proper analysis of the algorithms, we will also be desirable to study the performance.
This project will be supervised by Dr Joaquín Miguez.
For full details, see the project abstract: http://www.maths.qmul.ac.uk/sites/default/files/phd%20projects%202015/Prob/miguez.pdf
The application procedure is described on the School website. For further enquiries please contact Dr Joaquín Miguez ([email protected]
This project is eligible for several sources of full funding for the 2016/17 academic year, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process. The best candidates will be eligible to receive a prestigious Ian Macdonald Postgraduate Award of £1000, for which you will be considered alongside your application. The application deadline for full funding is January ti1st 2016.
There is also 50% funding scheme available for students who are able to find the matching 50 % of the cost of their studies. Competition for these half-funded slots will be less intensive, and eligible students should mention their willingness to be considered for them in their application. The application deadline for 50 % funding is January 31st 2016.
This project can be also undertaken as a self-funded project, either through your own funds or through a body external to Queen Mary University of London. Self-funded applications are accepted year-round.