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Noisy Hamiltonian Monte Carlo for doubly-intractable distributions

Authors: 

Juilian Stoehr, Alan Benson, Nial Friel

Publication Type: 
Refereed Original Article
Abstract: 
Hamiltonian Monte Carlo (HMC) has been progressively incorporated within the statistician’s toolbox as an alternative sampling method in settings when standard Metropolis-Hastings is inefficient. HMC generates a Markov chain on an augmented state space with transitions based on a deterministic differential flow derived from Hamiltonian mechanics. In practice, the evolution of Hamiltonian systems cannot be solved analytically, requiring numerical integration schemes. Under numerical integration, the resulting approximate solution no longer preserves the measure of the target distribution, therefore an accept-reject step is used to correct the bias. For doubly-intractable distributions – such as posterior distributions based on Gibbs random fields – HMC suffers from some computational difficulties: computation of gradients in the differential flow and computation of the accept-reject proposals poses difficulty. In this paper, we study the behaviour of HMC when these quantities are replaced by Monte Carlo estimates.
Digital Object Identifer (DOI): 
10.1080/10618600.2018.1506346
Publication Status: 
Published
Date Accepted for Publication: 
Monday, 12 February, 2018
Publication Date: 
22/03/2018
Journal: 
Journal of Computational and Graphical Statistics.
Institution: 
National University of Ireland, Dublin (UCD)
Open access repository: 
No