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Unbiased Hamiltonian Monte Carlo with couplings. (English) Zbl 1435.62287

Biometrika 106, No. 2, 287-302 (2019); erratum ibid. 107, No. 3, 769 (2020).
This paper designs unbiased estimators for Hamiltonian Monte Carlo and its variants. A method for parallelization of Hamiltonian Monte Carlo estimators based on building a pair of chains that are coupled in such a way that they meet exactly after some random but almost surely finite number of iterations is developed. These chains can then be combined. This allows for producing independent replicates in parallel and average them to obtain estimators that are consistent in the limit of the number of replicates. Scalability of the coupling in high dimensions is investigated. The efficiency of the proposed approach is illustrated on a logistic regression with 300 covariates and a log-Gaussian Cox point processes model.

MSC:

62J12 Generalized linear models (logistic models)
65C05 Monte Carlo methods
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