Wednesday 2nd November 2016
Ground Floor Seminar Room
25 Howland Street, London, W1T 4JG
Continuous-time MCMC and super-efficient Monte Carlo for big data
Current MCMC methods are based upon simulating a discrete-time Markov
chain. In this talk I will present an alternative approach to MCMC,
which simulates a continuous-time Markov process, called a piecewise
deterministic process. Originally such MCMC methods were motivated as
these are non-reversible processes, and it is commonly accepted that
non-reversible MCMC mixes better than (standard) reversible
The resulting continuous-time MCMC algorithms seems particularly
well-adapted for use in big data settings. The dynamics of the MCMC
process depend on the gradient of the log-posterior. This is
something that is easy to estimate using sub-sampling. Furthermore,
these continuous-time MCMC processes obey an "exact approximation"
property. Namely we can replace the gradient of the log-posterior by
an unbiased estimator of it, and the process will still sample from
the true posterior. Using low-variance estimators, which involve
sub-sampling the data and using control variates, can lead to an MCMC
sampler whose computational cost per effective sample size does not
increase with the number of data points.
This is joint work with Joris Bierkens and Gareth Roberts
Paul Fearnhead is currently Professor of Statistics at Lancaster University. His research encompasses Bayesian Statistics,
Monte Carlo methods, and Changepoint Detection, and he has been awarded the RSS Guy Medal in Bronze and the Adams prize.
He is currently involved in two EPSRC programme grants, i-like and StatScale, both looking at developing novel statistical methods suitable for modern big data challenges.