New developments in non-reversible Markov chain Monte Carlo

The exploration performed by a Markov chain Monte Carlo (MCMC) algorithm can be likened to the exploration of some interesting terrain. Traditional MCMC is `reversible': the simplicity of this condition has facilitated the huge number of extensions and variations on the standard MCMC algorithm that are available today; however reversibility also implies that on relatively flat terrain (and in real, high-dimensional applications only one direction is `uphill', with all other directions relatively flat), an MCMC `walker' loses their sense of direction so that their path becomes erratic and the exploration slow. By contrast, non-reversible MCMC keeps a sense of direction even over flat terrain. Current non-reversible algorithms come in two main flavours: one imagines a drone flying in a straight line above the terrain and occasionally changing direction so as to keep above the higher regions; the other inverts the terrain and imagines kicking a ball along it in a random direction. Both of these methods have great potential, but also practical problems that limit their usability. Drawing on both methods, this project will create new non-reversible algorithms which are much more efficient than standard, reversible, MCMC and can be applied across a wide variety of contexts; it will also create easy-to-use software for statistical practitioners. MCMC is used for the statistical analysis of complex data sets across a huge range of applications, from finance and fraud detection, through understanding, predicting and intervening in the spread of infectious diseases, to understanding the location of dark matter in the universe, and our work will benefit anyone analysing complex datasets in these and many other areas.