Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods

• 成果类型: Article
• 署名作者: Nishimura, Akihiko; Dunson, David B.; Lu, Jianfeng
• 署名单位: University of California System; University of California Los Angeles; Duke University; Duke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asz083
• 发表日期: 2020
• 页码: 365380
• 关键词: regression; equation

摘要

Hamiltonian Monte Carlo has emerged as a standard tool for posterior computation. In this article we present an extension that can efficiently explore target distributions with discontinuous densities. Our extension in particular enables efficient sampling from ordinal parameters through the embedding of probability mass functions into continuous spaces. We motivate our approach through a theory of discontinuous Hamiltonian dynamics and develop a corresponding numerical solver. The proposed solver is the first of its kind, with a remarkable ability to exactly preserve the Hamiltonian. We apply our algorithm to challenging posterior inference problems to demonstrate its wide applicability and competitive performance.