R. Neal. Handbook of Markov Chain Monte Carlo, (2010)
Аннотация
Hamiltonian dynamics can be used to produce distant proposals for the Metropolis
algorithm, thereby avoiding the slow exploration of the state space that results from
the diffusive behaviour of simple random-walk proposals. Though originating in
physics, Hamiltonian dynamics can be applied to most problems with continuous
state spaces by simply introducing fictitious “momentum” variables. A key to
its usefulness is that Hamiltonian dynamics preserves volume, and its trajectories
can thus be used to define complex mappings without the need to account for a
hard-to-compute Jacobian factor — a property that can be exactly maintained
even when the dynamics is approximated by discretizing time. In this review, I
discuss theoretical and practical aspects of Hamiltonian Monte Carlo, and present
some of its variations, including using windows of states for deciding on acceptance
or rejection, computing trajectories using fast approximations, tempering during
the course of a trajectory to handle isolated modes, and short-cut methods that
prevent useless trajectories from taking much computation time.
%0 Journal Article
%1 1206.1901
%A Neal, Radford M.
%D 2010
%J Handbook of Markov Chain Monte Carlo
%K Markov MonteCarlo
%P 113--162
%T MCMC Using Hamiltonian Dynamics
%V 54
%X Hamiltonian dynamics can be used to produce distant proposals for the Metropolis
algorithm, thereby avoiding the slow exploration of the state space that results from
the diffusive behaviour of simple random-walk proposals. Though originating in
physics, Hamiltonian dynamics can be applied to most problems with continuous
state spaces by simply introducing fictitious “momentum” variables. A key to
its usefulness is that Hamiltonian dynamics preserves volume, and its trajectories
can thus be used to define complex mappings without the need to account for a
hard-to-compute Jacobian factor — a property that can be exactly maintained
even when the dynamics is approximated by discretizing time. In this review, I
discuss theoretical and practical aspects of Hamiltonian Monte Carlo, and present
some of its variations, including using windows of states for deciding on acceptance
or rejection, computing trajectories using fast approximations, tempering during
the course of a trajectory to handle isolated modes, and short-cut methods that
prevent useless trajectories from taking much computation time.
@article{1206.1901,
abstract = {Hamiltonian dynamics can be used to produce distant proposals for the Metropolis
algorithm, thereby avoiding the slow exploration of the state space that results from
the diffusive behaviour of simple random-walk proposals. Though originating in
physics, Hamiltonian dynamics can be applied to most problems with continuous
state spaces by simply introducing fictitious “momentum” variables. A key to
its usefulness is that Hamiltonian dynamics preserves volume, and its trajectories
can thus be used to define complex mappings without the need to account for a
hard-to-compute Jacobian factor — a property that can be exactly maintained
even when the dynamics is approximated by discretizing time. In this review, I
discuss theoretical and practical aspects of Hamiltonian Monte Carlo, and present
some of its variations, including using windows of states for deciding on acceptance
or rejection, computing trajectories using fast approximations, tempering during
the course of a trajectory to handle isolated modes, and short-cut methods that
prevent useless trajectories from taking much computation time.
},
added-at = {2013-11-20T16:22:16.000+0100},
author = {Neal, Radford M.},
biburl = {https://www.bibsonomy.org/bibtex/233fcb1d5a6d675e371170820f0b4dbcd/giacomo.fiumara},
citeulike-article-id = {12118398},
interhash = {f26b3ec7720399d06a5c271916a0ee92},
intrahash = {33fcb1d5a6d675e371170820f0b4dbcd},
journal = {Handbook of Markov Chain Monte Carlo},
keywords = {Markov MonteCarlo},
pages = {113--162},
posted-at = {2013-03-06 23:35:00},
priority = {2},
timestamp = {2013-11-20T16:22:16.000+0100},
title = {{MCMC} Using {Hamiltonian} Dynamics},
volume = 54,
year = 2010
}