Stereographic Markov Chain Monte Carlo

arXiv:2205.12112v2 Announce Type: replace-cross
Abstract: High-dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves results in empirically observed ``stickiness'' and poor theoretical mixing properties -- lack of geometric ergodicity. In this paper, we introduce a new class of MCMC samplers that map the original high-dimensional problem in Euclidean space onto a sphere and remedy these notorious mixing problems. In particular, we develop random-walk …

abstract arxiv class combination gradient information markov mcmc paper spaces stat.co state stat.me stat.ml type