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Geometry and dynamics for Markov chain Monte Carlo

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Title: Geometry and dynamics for Markov chain Monte Carlo
Authors: Barp, A
Briol, F-X
Kennedy, AD
Girolami, M
Item Type: Journal Article
Abstract: Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of building chains which can explore probability densities efficiently. The method emerges from physics and geometry and these links have been extensively studied by a series of authors through the last thirty years. However, there is currently a gap between the intuitions and knowledge of users of the methodology and our deep understanding of these theoretical foundations. The aim of this review is to provide a comprehensive introduction to the geometric tools used in Hamiltonian Monte Carlo at a level accessible to statisticians, machine learners and other users of the methodology with only a basic understanding of Monte Carlo methods. This will be complemented with some discussion of the most recent advances in the field which we believe will become increasingly relevant to applied scientists.
Issue Date: 1-Mar-2018
Date of Acceptance: 1-Jun-2017
URI: http://hdl.handle.net/10044/1/53201
DOI: https://dx.doi.org/10.1146/annurev-statistics-031017-100141
ISSN: 2326-8298
Publisher: Annual Reviews
Start Page: 451
End Page: 471
Journal / Book Title: Annual Review of Statistics and Its Application
Volume: 5
Keywords: Science & Technology
Physical Sciences
Mathematics, Interdisciplinary Applications
Statistics & Probability
Mathematics
Markov chain Monte Carlo
information geometry
Hamiltonian mechanics
symplectic integrators
shadow Hamiltonians
INVERSE PROBLEMS
PHASE-SPACE
SIMULATION
ALGORITHMS
LANGEVIN
SYSTEMS
CONSTRUCTION
DIFFUSIONS
PARAMETERS
FERMIONS
stat.CO
cs.LG
hep-lat
math.NA
stat.ML
Publication Status: Published
Online Publication Date: 2017-12-08
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences



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