A geometric approach to informed MCMC sampling

Music City Center 

A Riemannian geometric framework for Markov chain Monte
Carlo (MCMC) is developed where using the Fisher-Rao metric on the
manifold of probability density functions (pdfs) informed proposal
densities for Metropolis-Hastings (MH) algorithms are constructed. We
exploit the square-root representation of pdfs under which the
Fisher-Rao metric boils down to the standard L2 metric, resulting in a
straightforward implementation of the proposed geometric MCMC
methodology. Unlike the random walk MH that blindly proposes a
candidate state using no information about the target, the geometric
MH algorithms effectively move an uninformed base density (e.g., a
random walk proposal density) towards different global/local
approximations of the target density. The superiority of the geometric
MH algorithm over other MCMC schemes is demonstrated using various
multimodal, nonlinear, and high-dimensional examples. A publicly
available R package geommc implements the proposed MCMC algorithms.

Markov chain Monte Carlo, Bayesian models