Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Mar 07, 2020
- Source ID
- 10.1093/biomet/asz083
Entities
People
- Akihiko Nishimura
- David B. Dunson
- Jianfeng Lu
Organizations
- Duke University
- National Science Foundation
- Office of Naval Research
- University of California, Los Angeles