SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Plenary Lecture


Off-Label Uses for ODE Methods: Randomization

R.D. Skeel and Y. Fang

Abstract
One of the most demanding calculations is to generate a single instance of a point in a high-dimensional configurational space from a specified probability distribution (with an unknown normalizing prefactor). (Being able to generate a dozen independent samples would solve grand challenge problems, such as protein folding.) Direct methods for doing this are impractical: one has to resort to using an iterative process known as a Markov chain Monte Carlo method, which converges only in the limit to the prescribed distribution. Such methods crawl through configuration space step by step, with acceptance of a step based on a Metropolis(-Hastings) criterion. An acceptance rate of 100% is possible in principle by embedding configuration space in a higher-dimensional phase space and using ODEs. In practice, numerical integrators must be used, lowering the acceptance rate, but at the same time allowing long moves. This is the essence of hybrid Monte Carlo methods. Presented is a general framework for constructing such methods under relaxed conditions.

Organized by         Universidad de Valladolid     IMUVA