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

**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.**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.

Szymon Urbas (March 2021-August 2021). New developments on non-reversible Markov chain Monte Carlo; EPSRC grant: EP/P033075/1.

Matthew Ludkin (November 2017-February 2021). New developments on non-reversible Markov chain Monte Carlo; EPSRC grant: EP/P033075/1.

Sam Holdstock

Tamas Papp

Year of completion in brackets.

Callum Vyner (2022):

*Contributions to Divide-and-Conquer MCMC."*Joint supervision with Prof. C. Nemeth.Szymon Urbas (2022):

*Bayesian inference and prediction for the inhomogeneous Poisson process, and a robust competitor to Hamiltonian Monte Carlo*; thesis. First destination: PDRA, VistaMilk SFI Research Centre, University College Dublin.Anna Barlow (2021):

*Flood Events: Extreme Value Problems and Efficient Estimation of Loss*; thesis. Joint supervision with Prof. J. Tawn. First destination: PDRA, Department of Mathematics and Statistics, Lancaster University.Sean Malory (2021):

*Bayesian inference for stochastic processes*; thesis. First destination: Data Scientist at AutoTrader.Katie Yates (2018):

*Low-density cluster separators for large, high-dimensional, mixed and non-linearly separable data*; thesis. Main supervisor: Dr. N. Pavlidis. First destination: Williams Formula One.Matthew Weldon (2017):

*School Choice, Competition and Ethnic Segregation in Lancashire: Evidence from structural models of two-sided matching*. Main supervisor: Dr. A.Titman. First destination: PDRA in Dept. Economics, Lancaster University.Shreena Patel (2016):

*Understanding consumer demand in customised pricing environments*; thesis. Joint supervision with Prof. P.Fearnhead. First destination: Data Scientist at Dunnhumby.Ioanna Lampaki (2015):

*Markov chain Monte Carlo methodology for inference on generalised linear spatial models*. First destination: Statistical applications developer, Dept. Physics, University of Edinbugh.Simon Taylor (2015):

*Motor Unit Number Estimation via Bayesian model selection and sequential Monte Carlo.*Joint supervision with Dr. G.Ridall. First destination: worked in industry for 6 months and then PDRA in Dept. M&S, Lancaster University.Stuart Sharples (2014).

*Predicting the delinquent behaviour of young people in Edinburgh*. Joint supervision with Dr. D. Costain. First destination: Temporary lecturer, Dept. M&S, Lancaster University.Tatiana Xifara (2013):

*Bayesian inference on a coupled hidden Markov model for disease interactions and a new position dependent Metropolis Adjusted Langevin Algorithm*. First destination: Visiting assistant professor, Dept. M&S, University of California Santa Cruz.Vasileios Giagos (2011):

*Inference for autoregulatory genetic networks using diffusion approximations*. Joint with Prof. P. Fearnhead. First destination: Temporary lecturer, Department of Mathematics and Statistics, Lancaster University.

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