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2013

Generalizing the No-U-Turn Sampler to Riemannian Manifolds

Betancourt, M. J.

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Hamiltonian Monte Carlo provides efficient Markov transitions at the expense of introducing two free parameters: a step size and total integration time.

Because the step size controls discretization error it can be readily tuned to achieve certain accuracy criteria, but the total integration time is left unconstrained.
Recently Hoffman and Gelman proposed a criterion for tuning the integration time in certain systems with their No U-Turn Sampler, or NUTS.
In this paper I investigate the dynamical basis for the success of NUTS and generalize it to Riemannian Manifold Hamiltonian Monte Carlo.

Generalizing the No-U-Turn Sampler to Riemannian Manifolds · Around

Built on

Geometrical Methods of Mathematical Physics
B. Schutz, · 1980
Earlier work this paper cites.
Physics Letters B 195
S. Duane, A. Kennedy, B. J. Pendleton, and D. Roweth, · 1987
Earlier work this paper cites.
Classical Dynamics: A Contemporary Approach
J. V. José and E. J. Saletan, · 1998
Earlier work this paper cites.
Computational Statistics 14
H. Haario, E. Saksman, and J. Tamminen, · 1999
Earlier work this paper cites.

Similar

Mcmc using hamiltonian dynamics,
R. Neal, · 2011
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M. J. Betancourt and L. C. Stein, · 2011
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ArXiv e-prints (2011), 1111.4246
M. D. Hoffman and A. Gelman, · 2011
Cited alongside, same era.

Then

Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73
M. Girolami and B. Calderhead, · 2011
Later among the works it cites.
ArXiv e-prints (2012), 1212.4693
M. J. Betancourt, · 2012
Later among the works it cites.
Stan: A c++ library for probability and sampling, version 1.0, 2012
Stan Development Team, · 2012
Later among the works it cites.

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