Hybrid Monte Carlo on Hilbert spaces

摘要: The Hybrid Monte Carlo (HMC) algorithm provides a framework for sampling from complex, high-dimensional target distributions. In contrast with standard Markov chain (MCMC) algorithms, it generates nonlocal, nonsymmetric moves in the state space, alleviating random walk type behaviour simulated trajectories. However, similarly to algorithms based on or Langevin proposals, number of steps required explore distribution typically grows dimension space. We define generalized HMC which overcomes this problem measures arising as finite-dimensional approximations π have density respect Gaussian measure an infinite-dimensional Hilbert key idea is construct MCMC method well defined space itself. We successively address following issues setting space: (i) construction probability Π enlarged phase having marginal, together Hamiltonian flow that preserves Π; (ii) development suitable geometric numerical integrator flow; and (iii) derivation accept/reject rule ensure preservation when using above instead actual flow. Experiments are reported compare new version