The Hybrid Monte Carlo Algorithm on Hilbert Space
Seminar Room 1, Newton Institute
Hybrid Monte Carlo methods are a class of algorithms for sampling probability measures defined via a density with respect to Lebesgue measure. However, in many applications the probability measure of interest is on an infinite dimensional Hilbert space and is defined via a density with respect to a Gaussian measure. I will show how the Hybrid Monte Carlo methodology can be extended to this Hilbert space setting. A key building block is the study of measure preservation properties for certain semilinear partial differential equations of Hamiltonian type, and approximation of these equations by volume-preserving integrators.
Joint work with A. Beskos (UCL), F. Pinski (Cincinnati) and J.-M. Sanz-Serna (Valladolid).