Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods

Akihiko Nishimura, David B Dunson and Jianfeng Lu

Biometrika, 2020, vol. 107, issue 2, 365-380

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.

Keywords: Bayesian inference; Geometric numerical integration; Markov chain Monte Carlo; Measure-valued differential equation (search for similar items in EconPapers)
Date: 2020
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1093/biomet/asz083 (application/pdf)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:oup:biomet:v:107:y:2020:i:2:p:365-380.

Ordering information: This journal article can be ordered from
https://academic.oup.com/journals

Access Statistics for this article

Biometrika is currently edited by Paul Fearnhead

More articles in Biometrika from Biometrika Trust Oxford University Press, Great Clarendon Street, Oxford OX2 6DP, UK.
Bibliographic data for series maintained by Oxford University Press ().