Super-Efficient Exact Hamiltonian Monte Carlo for the von Mises Distribution

Abstract

Markov Chain Monte Carlo algorithms, the method of choice to sample from generic high-dimensional distributions, are rarely used for continuous one-dimensional distributions, for which more effective approaches are usually available (e.g. rejection sampling). In this work we present a counter-example to this conventional wisdom for the von Mises distribution, a maximum-entropy distribution over the circle. We show that Hamiltonian Monte Carlo with Laplacian momentum has exactly solvable equations of motion and, with an appropriate travel time, the Markov chain has negative autocorrelation at odd lags for odd observables and yields a relative effective sample size bigger than one.

5 pages, 4 figures

References in corpus (4)

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• Rejection-free Monte-Carlo sampling for general potentials
• Discontinuous Hamiltonian Monte Carlo for discrete parameters and discontinuous likelihoods
• A piecewise deterministic scaling limit of Lifted Metropolis-Hastings in the Curie-Weiss model