scholarly journals Variable transformation to obtain geometric ergodicity in the random-walk Metropolis algorithm

2012 ◽  
Vol 40 (6) ◽  
pp. 3050-3076 ◽  
Author(s):  
Leif T. Johnson ◽  
Charles J. Geyer
Keyword(s):  
Random Walk ◽  
Metropolis Algorithm ◽  
Geometric Ergodicity ◽  
Variable Transformation ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

On the geometric ergodicity of hybrid samplers

2003 ◽  
Vol 40 (1) ◽  
pp. 123-146 ◽  
Author(s):  
G. Fort ◽  
E. Moulines ◽  
G. O. Roberts ◽  
J. S. Rosenthal
Keyword(s):  
Random Walk ◽  
Sufficient Conditions ◽  
Metropolis Algorithm ◽  
Geometric Ergodicity ◽  
Target Density ◽  
Symmetric Random Walk ◽  
Uniform Ergodicity ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

In this paper, we consider the random-scan symmetric random walk Metropolis algorithm (RSM) on ℝd. This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full-dimensional symmetric random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sufficient conditions implying V-uniform ergodicity of the RSM when the target density decreases either subexponentially or exponentially in the tails.

On the geometric ergodicity of hybrid samplers

2003 ◽  
Vol 40 (01) ◽  
pp. 123-146 ◽  
Author(s):  
G. Fort ◽  
E. Moulines ◽  
G. O. Roberts ◽  
J. S. Rosenthal
Keyword(s):  
Random Walk ◽  
Sufficient Conditions ◽  
Metropolis Algorithm ◽  
Geometric Ergodicity ◽  
Target Density ◽  
Symmetric Random Walk ◽  
Uniform Ergodicity ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

In this paper, we consider the random-scan symmetric random walk Metropolis algorithm (RSM) on ℝ d . This algorithm performs a Metropolis step on just one coordinate at a time (as opposed to the full-dimensional symmetric random walk Metropolis algorithm, which proposes a transition on all coordinates at once). We present various sufficient conditions implying V-uniform ergodicity of the RSM when the target density decreases either subexponentially or exponentially in the tails.

scholarly journals Asymptotic analysis of the random walk Metropolis algorithm on ridged densities

2018 ◽  
Vol 28 (5) ◽  
pp. 2966-3001 ◽  
Author(s):  
Alexandros Beskos ◽  
Gareth Roberts ◽  
Alexandre Thiery ◽  
Natesh Pillai
Keyword(s):  
Random Walk ◽  
Asymptotic Analysis ◽  
Metropolis Algorithm ◽  
Random Walk Metropolis ◽  
Random Walk Metropolis Algorithm

scholarly journals Ergodicity of Markov chain Monte Carlo with reversible proposal

2017 ◽  
Vol 54 (2) ◽  
pp. 638-654 ◽  
Author(s):  
K. Kamatani
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Random Walk ◽  
Markov Chain Monte Carlo ◽  
Geometric Ergodicity ◽  
Suitable Transformation ◽  
Ergodic Properties ◽  
Random Walk Metropolis ◽  
Heavy Tailed ◽  
Random Walk Metropolis Algorithm

Abstract We describe the ergodic properties of some Metropolis–Hastings algorithms for heavy-tailed target distributions. The results of these algorithms are usually analyzed under a subgeometric ergodic framework, but we prove that the mixed preconditioned Crank–Nicolson (MpCN) algorithm has geometric ergodicity even for heavy-tailed target distributions. This useful property comes from the fact that, under a suitable transformation, the MpCN algorithm becomes a random-walk Metropolis algorithm.

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