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PhD Projects

If you are interested in studying for a PhD with me then please contact me. Example research areas include:

  1. Non-reversible MCMC. Standard MCMC is reversible: on a uniform target, for example, the probability of moving from A to B is the same as the probability of moving from B to A. Hence there is a natural tendency for the algorithm to meander, with a distance proportional to n^1/2 covered in n iterations. Interesting non-reversible MCMC algorithms retain a sense of direction and have the potential for exploring the space much more efficiently. Examples include Hamiltonion Monte Carlo and the discrete bouncy particle sampler as well at continuous-time algorithms such as the bouncy particle sampler and the zig-zag sampler. An example project might look at developing a new non-reversible algorithm and applying it to some interesting application type.

  2. MCMC for reaction networks. Consider a set of species: this could be literal, such as foxes and rabbits, or a protein and its dimer, or could be classes such as people susceptible to a disease, people infected with a disease and people who have recovered from the disease. The different species interact through "reactions" (e.g. a fox eats a rabbit) and the rate of these reactions depends on the current numbers of the relevant species (e.g. the more foxes and rabbits there are, the more rabbits are eaten each day). A reaction network is the continuous-time Markov chain whose state is the current number of each species. Interest may lie in the forms of the reactions and their rates, in the current or historical species numbers, future prediction, or even all three. An example project might create a new, more efficient inference methodology for a subclass of reaction networks and apply to an autoregulatory gene network or a disease epidemic.


Current PhD Students

Past PhD Students

Year of completion in brackets.