Monte Carlo Seminar| Vivek Roy|A Riemannian manifold approach to informed MCMC sampling|May 20, 2025 скачать в хорошем качестве

Monte Carlo Seminar| Vivek Roy|A Riemannian manifold approach to informed MCMC sampling|May 20, 2025

Online Monte Carlo Seminar Website: sites.google.com/view/monte-carlo-seminar/ Speaker: Vivekananda Roy (Iowa State University) Title: A Riemannian manifold approach to informed MCMC sampling Abstract: 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.