Universality of the Langevin diffusion as scaling limit of a family of Metropolis-Hastings processes I: fixed dimension

Weak convergence and optimal scaling of random walk Metropolis algorithms

Original

G. O. Roberts, A. Gelman, and W. R. Gilks · 1907

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Markov processes

S. N. Ethier and T. G. Kurtz · 1986

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Weak convergence of Markov chain sampling methods and annealing algorithms to diffusions

S. B. Gelfand and S. K. Mitter · 1991

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A geometric interpretation of the Metropolis-Hastings algorithm

L. J. Billera and P. Diaconis · 2001

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Optimal scaling for various Metropolis-Hastings algorithms

G. O. Roberts and J. S. Rosenthal · 2001

Cited alongside, same era.

General state space Markov chains and MCMC algorithms

G. O. Roberts and J. S. Rosenthal · 2004

Cited alongside, same era.

Weak convergence of Metropolis algorithms for non-i.i.d. target distributions

M. Bédard · 2007

Cited alongside, same era.

Diffusion limits of the random walk Metropolis algorithm in high dimensions

J. C. Mattingly, N. S. Pillai, and A. M. Stuart · 2012

Cited alongside, same era.

Metropolis-Hastings reversiblizations of non-reversible Markov chains

M. C. Choi

Cited in the paper.

Universality of the Langevin diffusion as scaling limit of a family of Metropolis-Hastings processes II: the Curie-Weiss model

M. C. Choi

Cited in the paper.

Optimal scaling for the transient phase of Metropolis Hastings algorithms: the longtime behavior

B. Jourdain, T. Lelièvre, and B. a. Miasojedow · 2014

Later among the works it cites.

A piecewise deterministic scaling limit of lifted Metropolis-Hastings in the Curie-Weiss model

J. Bierkens and G. Roberts · 2017

Later among the works it cites.

On hitting time, mixing time and geometric interpretations of Metropolis-Hastings reversiblizations

M. C. Choi and L.-J. Huang · 2019

Closest in time.