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Recent work incorporating geometric ideas in Markov chain Monte Carlo is reviewed in order to highlight these advances and their possible application in a range of domains beyond Statistics.
Information and accuracy attainable in the estimation of statistical parameters
C Radhakrishna Rao · 1945
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An invariant form for the prior probability in estimation problems
Harold Jeffreys · 1946
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Differential geometry of curves and surfaces
Manfredo Perdigao Do Carmo and Manfredo Perdigao Do Carmo · 1976
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Time-reversible diffusions
John Kent · 1978
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Geometrical methods of mathematical physics
Bernard F. Schutz · 1984
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Central limit theorem for additive functionals of reversible markov processes and applications to simple exclusions
C Kipnis and SRS Varadhan · 1986
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The role of differential geometry in statistical theory
OE Barndorff-Nielsen, DR Cox, and N Reid · 1986
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An introduction to differentiable manifolds and Riemannian geometry
William M Boothby · 1986
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A generalized guided monte carlo algorithm
Alan M Horowitz · 1991
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Inference from iterative simulation using multiple sequences
Andrew Gelman and Donald B Rubin · 1992
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Riemannian geometry
Manfredo P Do Carmo · 1992
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Stability of markovian processes ii: Continuous-time processes and sampled chains
Sean P Meyn and Richard L Tweedie · 1993
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Preferred point geometry and statistical manifolds
Frank Critchley, Paul Marriott, Mark Salmon, et al · 1993
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Markov chains for exploring posterior distributions
Luke Tierney · 1994
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Geometric convergence and central limit theorems for multidimensional hastings and metropolis algorithms
Gareth O Roberts and Richard L Tweedie · 1996
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Rates of convergence of the hastings and metropolis algorithms
Kerrie L Mengersen and Richard L Tweedie · 1996
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Exponential convergence of langevin distributions and their discrete approximations
Gareth O Roberts and Richard L Tweedie · 1996
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Applications of differential geometry to econometrics
Paul Marriott and Mark Salmon · 2000
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Geometric ergodicity of metropolis algorithms
Søren Fiig Jarner and Ernst Hansen · 2000
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Diffusions, Markov processes and martingales: Volume 2, Itô calculus
L Chris G Rogers and David Williams · 2000
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Honest exploration of intractable probability distributions via markov chain monte carlo
Galin L Jones and James P Hobert · 2001
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Optimal scaling for various metropolis-hastings algorithms
Gareth O Roberts, Jeffrey S Rosenthal, et al · 2001
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In all likelihood: statistical modelling and inference using likelihood
Yudi Pawitan · 2001
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On choosing and bounding probability metrics
Alison L Gibbs and Francis Edward Su · 2002
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Langevin diffusions and metropolis-hastings algorithms
Gareth O Roberts and Osnat Stramer · 2002
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On the local geometry of mixture models
Paul Marriott · 2002
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The imbedding problem for riemannian manifolds
JOHN F NASH JR · 2002
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Stochastic analysis on manifolds
Elton P Hsu · 2002
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Computing the nearest correlation matrix—a problem from finance
Mcmc using hamiltonian dynamics
R Neal · 2011
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The geometry of hamiltonian monte carlo
Michael Betancourt and Leo C Stein · 2011
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Multivariable calculus
James Stewart · 2011
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Statistical analysis of nonlinear dynamical systems using differential geometric sampling methods
Ben Calderhead and Mark Girolami · 2011
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Efficient probabilistic model personalization integrating uncertainty on data and parameters: Application to eikonal-diffusion models in cardiac electrophysiology
Ender Konukoglu, Jatin Relan, Ulas Cilingir, Bjoern H Menze, Phani Chinchapatnam, Amir Jadidi, Hubert Cochet, Meleze Hocini, Hervé Delingette, Pierre Jaïs, et al · 2011
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Nicholas J Higham · 2002
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Stochastic differential equations
Bernt Øksendal · 2003
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Smooth manifolds
John M Lee · 2003
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Monte Carlo statistical methods
Christian P Robert and George Casella · 2004
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On the markov chain central limit theorem
Galin L Jones et al · 2004
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The Langevin equation: with applications to stochastic problems in physics, chemistry, and electrical engineering
William Coffey, Yu P Kalmykov, and John T Waldron · 2004
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Discussion on ‘riemann manifold langevin and hamiltonian monte carlo methods’ (by girolami, m. and calderhead, b.)
Krzystof Latuszynski, Gareth O. Roberts, Alexandre Thiery, and Katarzyna Wolny · 2011
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A stochastic newton mcmc method for large-scale statistical inverse problems with application to seismic inversion
James Martin, Lucas C Wilcox, Carsten Burstedde, and Omar Ghattas · 2012
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Hamiltonian monte carlo for hierarchical models
MJ Betancourt and Mark Girolami · 2013
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Optimal scaling of the random walk metropolis: general criteria for the 0.234 acceptance rule
Chris Sherlock et al · 2013
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Advanced mcmc methods for sampling on diffusion pathspace
Alexandros Beskos, Konstantinos Kalogeropoulos, and Erik Pazos · 2013
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Langevin diffusions and the metropolis-adjusted langevin algorithm
Tatiana Xifara, Chris Sherlock, Samuel Livingstone, Simon Byrne, and Mark Girolami · 2013
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A primer on stochastic differential geometry for signal processing
Jonathan H Manton · 2013
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Noemi Petra, James Martin, Georg Stadler, and Omar Ghattas · 2013
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A general metric for riemannian manifold hamiltonian monte carlo
Michael Betancourt · 2013
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Kernel adaptive metropolis-hastings
Dino Sejdinovic, Maria Lomeli Garcia, Heiko Strathmann, Christophe Andrieu, and Arthur Gretton · 2013
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Markov chain monte carlo inference for markov jump processes via the linear noise approximation
Vassilios Stathopoulos and Mark A Girolami · 2013
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Mcmc methods for functions: modifying old algorithms to make them faster
SL Cotter, GO Roberts, AM Stuart, David White, et al · 2013
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Proposals which speed up function-space mcmc
Kody JH Law · 2013
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A function space hmc algorithm with second order langevin diffusion limit
Michela Ottobre, Natesh S Pillai, Frank J Pinski, and Andrew M Stuart · 2013
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Geodesic monte carlo on embedded manifolds
Simon Byrne and Mark Girolami · 2013
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Sampling from a manifold
Persi Diaconis, Susan Holmes, Mehrdad Shahshahani, et al · 2013
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