scholarly journals Diffusion limits of the random walk Metropolis algorithm in high dimensions

2012 ◽  
Vol 22 (3) ◽  
pp. 881-930 ◽  
Author(s):  
Jonathan C. Mattingly ◽  
Natesh S. Pillai ◽  
Andrew M. Stuart
Keyword(s):  
Random Walk ◽  
Metropolis Algorithm ◽  
High Dimensions ◽  
Random Walk Metropolis ◽  
Diffusion Limits ◽  
Random Walk Metropolis Algorithm

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

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 Comparison of hit-and-run, slice sampler and random walk Metropolis

2018 ◽  
Vol 55 (4) ◽  
pp. 1186-1202
Author(s):  
Daniel Rudolf ◽  
Mario Ullrich
Keyword(s):  
Random Walk ◽  
Markov Chains ◽  
Metropolis Algorithm ◽  
Partial Ordering ◽  
Markov Operators ◽  
Random Walk Metropolis ◽  
Slice Sampler ◽  
Hit And Run ◽  
Random Walk Metropolis Algorithm ◽  
Sampling Procedures

Abstract Different Markov chains can be used for approximate sampling of a distribution given by an unnormalized density function with respect to the Lebesgue measure. The hit-and-run, (hybrid) slice sampler, and random walk Metropolis algorithm are popular tools to simulate such Markov chains. We develop a general approach to compare the efficiency of these sampling procedures by the use of a partial ordering of their Markov operators, the covariance ordering. In particular, we show that the hit-and-run and the simple slice sampler are more efficient than a hybrid slice sampler based on hit-and-run, which, itself, is more efficient than a (lazy) random walk Metropolis algorithm.

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