title: Applying diffusion-based Markov chain Monte Carlo.
abstract: We examine the performance of a strategy for Markov chain Monte Carlo (MCMC) developed by simulating a discrete approximation to a stochastic differential equation (SDE). We refer to the approach as diffusion MCMC. A variety of motivations for the approach are reviewed in the context of Bayesian analysis. In particular, implementation of diffusion MCMC is very simple to set-up, even in the presence of nonlinear models and non-conjugate priors. Also, it requires comparatively little problem-specific tuning. We implement the algorithm and assess its performance for both a test case and a glaciological application. Our results demonstrate that in some settings, diffusion MCMC is a faster alternative to a general Metropolis-Hastings algorithm.
authors.affiliation: The Ohio State University, Department of Statistics, Columbus, OH, United States of America.
authors.forename: Radu
authors.identifier: http://orcid.org/0000-0002-7791-8560
authors.initials: R
authors.lastname: Herbei
authors.affiliation: Western Michigan University, Department of Statistics, Kalamazoo, MI, United States of America.
authors.forename: Rajib
authors.initials: R
authors.lastname: Paul
authors.affiliation: The Ohio State University, Department of Statistics, Columbus, OH, United States of America.
authors.forename: L Mark
authors.initials: LM
authors.lastname: Berliner
mesh_terms: D001499:Bayes Theorem; D008390:Markov Chains; D009010:Monte Carlo Method; D013269:Stochastic Processes