### Sebastian Reich

Department of Mathematics, University of Potsdam, Germany

### GSHMC: An efficient Markov chain Monte Carlo sampling method

**Wednesday 29th October 14:05-14:55pm,
Eastern Avenue Lecture Theatre. **
Markov chain Monte Carlo (MCMC) methods are often the method of choice when it comes to sample for a high dimensional probability distribution function (PDF). While MCMC method offer great flexibility and can be widely applied, they also often suffer from a high correlation between samples which leads to a slow exploration of phase space. The hybrid Monte Carlo method (HMC) is an attractive variant of MCMC because it allows, in principle, to take large steps in phase space. The key underlying idea is to formulate a deterministic dynamical system which possesses the desired PDF as an
invariant. While this leads to a 100 % acceptance rate in theory, numerical implementations reduce the acceptance rate with increasing system size and large discretization parameters.

In my talk I will first provide a brief introduction the HMC and related methods. I will then show how the inherent geometry of the underlying dynamical system and its numerical approximation can be used to avoid a reduction in the acceptance rates even for highly non-local proposal steps. This leads to the generalized shadow hybrid Monte Carlo (GSHMC) method. Results from molecular dynamics simulations of a membrane protein will be shown (joint work with Fujitsu Laboratories Europe and biochemistry Oxford).

HMC and related methods can also be interpreted as statistically correct implementations of Langevin/Brownian dynamics. I will comment on this aspect of HMC in the final part of my talk.