Non-reversible Markov chain Monte Carlo algorithms such as Piecewise Deterministic Markov Processes are becoming increasingly popular in Bayesian computation as well as Physics. One of the attractions of these methods is that they provide momentum which facilitates mixing through the state space. This talk will discuss some results which describe the extent to which the advantages of non-reversible MCMC persist in high-dimensional problems. In some cases the momentum can be homogenised in the high-dimensional limit to give diffusive behaviour. This work is applied to a comparison of reversible and non-reversible simulated (and parallel) tempering algorithms. Practical implementational guidance for these algorithms is given by the theory.

This is joint work with Jeff Rosenthal.