Home - Publications - Supervision - Teaching
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 in non-reversible Markov chain Monte Carlo; EPSRC grant: EP/P033075/1.
Matthew Ludkin (November 2017-February 2021). New developments in non-reversible Markov chain Monte Carlo; EPSRC grant: EP/P033075/1.
Lanya Yang
Max Howell
Sam Holdstock
Year of completion in brackets.
Tamas Papp (2026): Methodology and theory for unbiased Markov chain Monte Carlo and alternatives; thesis. First destination: PDRA, National University of Singapore. EEs: Pierre Jacob and Peter Neal.
Callum Vyner (2022): Contributions to Divide-and-Conquer MCMC; thesis. Joint supervision with Prof. C. Nemeth. EE: Darren Wilkinson
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. EE: Alex Beskos
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. EE: Adam Johansen.
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. EE: Richard Boys.
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. EE: Duncan Lee.
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. EE: Andrew Golightly.
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. EE: Irini Moustaki.
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. EE: Ruth King.
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. EE: Darren Wilkinson.
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