Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods. (7th March 2020)

• Record Type: Journal Article
• Authors: Nishimura, Akihiko; Dunson, David B; Lu, Jianfeng
• Is Part Of: Biometrika. Volume 107:Number 2(2020:Jun.)
• Page Start: 365
• Page End: 380
• Publication Date: 2020-03-07
• Subjects: Bayesian inference -- Geometric numerical integration -- Markov chain Monte Carlo -- Measure-valued differential equation; Biometry -- Periodicals; 570.1519505
• DOI: 10.1093/biomet/asz083
• Languages: English
• ISSNs: 0006-3444

Abstract

Summary: 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.