Fetching the paper…

Reading the bibliography…

2011

The Geometry of Hamiltonian Monte Carlo

Betancourt, Michael, Stein, Leo C.

Original
PDF
Post on X

Understand

With its systematic exploration of probability distributions, Hamiltonian Monte Carlo is a potent Markov Chain Monte Carlo technique; it is an approach, however, ultimately contingent on the choice of a suitable Hamiltonian function.

By examining both the symplectic geometry underlying Hamiltonian dynamics and the requirements of Markov Chain Monte Carlo, we construct the general form of admissible Hamiltonians and propose a particular choice with potential application in Bayesian inference.

The Geometry of Hamiltonian Monte Carlo · Around

Built on

B. Schutz, Geometrical Methods of Mathematical Physics (Cambridge University Press, New York, 1980)
1980
Earlier work this paper cites.
A. Weinstein, J. Differential Geom. 18
1983
Earlier work this paper cites.
S. Duane, A. Kennedy, B. J. Pendleton, and D. Roweth, Physics Letters B 195
1987
Earlier work this paper cites.
G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins University Press, Baltimore, 1996)
1996
Earlier work this paper cites.

Similar

G. B. Folland, Real Analysis: Modern Techniques and Their Applications (1999)
1999
Cited alongside, same era.
B. Leimkuhler and S. Reich, Simulating Hamiltonian Dynamics (Cambridge University Press, New York, 2004)
2004
Cited alongside, same era.
O. Calin and D. C. Chang, Geometric Mechanics on Reimannian Manifolds (Birkhäuser, New York, 2004)
2004
Cited alongside, same era.
M. Kardar, Statistical Mechanics of Particles (Cambridge University Press, New York, 2007)
2007
Cited alongside, same era.

Then

R. Neal, in Handbook of Markov Chain Monte Carlo , edited by S. Brooks, A. Gelman, G. L. Jones, and X.-L. Meng (CRC Press, New York, 2011)
2011
Closest in time.
M. Girolami and B. Calderhead, Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73
2011
Closest in time.
M. Betancourt, in Maximum Entropy and Bayesian methods in science and engineering , American Institute of Physics Conference Series, Vol. 1305, edited by A. Mohammad-Djafari, J.-F. Bercher, & P. Bessiére (AIP Press, 2011) pp. 165–172, arXiv:1005.0157 [physics.data-an]
Original
2011
Closest in time.

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…