A Novel Hybrid Monte Carlo Algorithm for Sampling Path Space

To sample from complex, high-dimensional distributions, one may choose algorithms based on the Hybrid Monte Carlo (HMC) method. HMC-based generate nonlocal moves alleviating diffusive behavior. Here, I build an already defined HMC framework, hybrid Hilbert spaces (Beskos, et al. Stoch. Proc. Applic. 2011), that provides finite-dimensional approximations of measures π, which have density with respect to a Gaussian measure infinite-dimensional (path) space. In all algorithms, has some freedom mass operator. The novel feature algorithm described in this article lies choice This new defines Markov Chain (MCMC) method is well space itself. As before, herein uses enlarged phase Π having target π as marginal, together Hamiltonian flow preserves Π. previous work, authors explored where was augmented Brownian bridges. With choice, by Ornstein–Uhlenbeck (OU) covariance bridges grows its length, negative effects acceptance rate MCMC contrasts OU bridges, independent path length. ingredients include definition operator, equations for flow, (approximate) numerical integration evolution equations, and finally, Metropolis–Hastings rule. Taken together, these constitute robust sampling distribution almost dimension-free manner. behavior demonstrated computer experiments particle moving two dimensions, between free-energy basins separated entropic barrier.