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Activity Number: 351
Type: Topic Contributed
Date/Time: Tuesday, August 2, 2016 : 10:30 AM to 12:20 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #318751 View Presentation
Title: Geometrically Tempered Hamiltonian Monte Carlo
Author(s): Akihiko Nishimura* and David Dunson
Companies: Duke University and Duke University
Keywords: Hamiltonian Monte Carlo ; Riemannian geometry ; tempering ; multimodal ; geometric integrator ; Markov chain Monte Carlo

Hamiltonian Monte Carlo (HMC) has become routinely used for sampling from posterior distributions. Its extension Riemann manifold HMC (RMHMC) modifies the proposal kernel through distortion of local distances by a Riemannian metric. The performance depends critically on the choice of metric, with Fisher information providing the standard choice. In this article, we propose a new class of metrics aimed at improving HMC's performance on multi-modal target distributions. We refer to the proposed approach as geometrically tempered HMC (GTHMC) due to its connection to other tempering methods. We establish a geometric theory behind RMHMC to motivate GTHMC and characterize its theoretical properties. Moreover, we develop a novel variable step size integrator for simulating Hamiltonian dynamics to improve on the usual Stormer-Verlet integrator which suffers from numerical instability in GTHMC settings. We illustrate GTHMC through simulations, demonstrating generality and substantial gains over standard HMC implementations in terms of effective sample size.

Authors who are presenting talks have a * after their name.

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