This page lists some research topics that I am interested in and that could be the basis for undergraduate or postgraduate research projects.

MCMC sampling on manifolds

I am interested in Markov chain Monte Carlo sampling schemes on state spaces X that are (potentially high-dimensional) manifolds arising in spatial statistics, directional stattistics, and shape analysis, e.g. spheres, Stiefel manifolds, and Kendall shape spaces.

Onsager–Machlup theory

I am interested in the local behaviour of measures μ on metric spaces X. For some measures μ, their local behaviour can be quantified using an Onsager–Machlup functional I_μ : X → ℝ which, at least in simple cases, behaves like a formal negative log-density for μ. It is interesting to try and derive and manipulate Onsager–Machlup functionals for more exotic measures, e.g. ones supported on manifolds, fractals, or infinite-dimensional spaces.

Time series analysis

I am interested in theory and methods for the analysis of time series, especially those with high-dimensional or functional outputs.