My research interests lie in the development of general Bayesian statistical methodology, with applications for quantifying uncertainty and reasoning about hypothesised mechanisms in biological systems.
My PhD was in the field of Computational Statistics and was funded by a Microsoft Research European PhD Scholarship. During this time, I developed novel Markov chain Monte Carlo methodology that exploits the natural representation of the parameter space of a statistical model as a Riemannian manifold. In my doctoral thesis I demonstrated how to derive generalisations of the Metropolis-adjusted Langevin algorithm and the Hybrid Monte Carlo algorithm defined on a Riemannian manifold. The resulting algorithms allow for efficient Bayesian statistical inference over many classes of statistical models and resolve many shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlation structure. In particular I considered examples of Bayesian inference on logistic regression models, log-Gaussian Cox point process models, stochastic volatility models, and both parameter and model level inference of dynamical systems described by nonlinear differential equations.
Current motivation for my work includes the rational and systematic comparison of competing model hypotheses to describe signalling pathways associated with chronic myeloid leukaemia, and statistical modelling of ion channels. In particular the aim is to identify the kinetic mechanisms responsible for ion channel control. Like any protein, a channel exists in several conformational states, and activation (by voltage changes or by neurotransmitters) takes it through a series of shut conformations to the active open states. The process and the dwell times of the protein in these states can be well modelled probabilistically as an aggregated Markov process.
Unusually for a biological system, one can obtain vast numbers of relatively accurate measurements of open and closed states on an incredibly small time scale. However, despite the large numbers of observations of the open/shut states of the ion channel, there is still much uncertainty regarding the underlying model. There may be missing observations due to the time resolution of the measurements, and in reality there are a number of different underlying open/shut states of the receptor that are indistinguishable in experimental investigation. Current state of the art approaches for analysing these models are based on maximum likelihood estimation of the rate parameters, and model comparison proceeds in a somewhat ad hoc manner, often based on visual representations of the model fits.
Throughout this Research Fellowship I shall be developing and applying statistical inferential methods based on the geometry of this type of complex model, in order to address the main challenges of parameter identifiability, multimodality, and in particular systematic model comparison in a hypothesis driven manner. This direction of research, combined with structural work, arguably provides the best chance of reliably inferring structure-activity relationships, which should greatly contribute to the ultimate (but still unachieved) goal of rational drug design.
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