Dimension-independent likelihood-informed MCMC

Many Bayesian inference problems require exploring the posterior distribution of high-dimensional parameters that, in principle, can be described as functions. This work introduces a family of Markov chain Monte Carlo (MCMC) samplers that can adapt to the particular structure of a posterior distribution over functions. Two distinct lines of research intersect in the methods developed here. First, we introduce a general class of operator-weighted proposal distributions that are well defined on function space, such that the performance of the resulting MCMC samplers is independent of the discretization of the function. Second, by exploiting local Hessian information and any associated lowdimensional structure in the change from prior to posterior distributions, we develop an inhomogeneous discretization scheme for the Langevin stochastic differential equation that yields operator-weighted proposals adapted to the non-Gaussian structure of the posterior. The resulting dimension-independ...

• Type: Journal
• Year: 2016
• Where: JCPHY
• Authors: Tiangang Cui, Kody J. H. Law, Youssef M. Marzouk
• Keywords: JCPHY 2016