Applied Maths Seminar: Reich -- GSHMC: An efficient Markov chain Monte Carlo sampling method

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.  

http://www.maths.usyd.edu.au/u/AppliedSeminar/abstracts/2008/reich.html