STEREOGRAPHIC MARKOV CHAIN MONTE CARLO

• 成果类型: Article
• 署名作者: Yang, Jun; Latuszynski, Krzysztof; Roberts, Gareth o.
• 署名单位: University of Copenhagen; University of Warwick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2426
• 发表日期: 2024
• 页码: 2692-2713
• 关键词: geometric ergodicity; SCALING LIMITS; CONVERGENCE; hastings; algorithms; MANIFOLDS; dimension

摘要

High-dimensional distributions, especially those with heavy tails, are 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 Metropolis type algorithms as well as versions of the Bouncy Particle Sampler that are uniformly ergodic for a large class of light and heavy-tailed distributions and also empirically exhibit rapid convergence in high dimensions. In the best scenario, the proposed samplers can enjoy the blessings of dimensionality that the convergence is faster in higher dimensions.