Efficiency of delayed-acceptance random walk Metropolis algorithms

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.

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On the geometric ergodicity of hybrid samplers

Journal of Applied Probability ◽

10.1017/s0021900200022300 ◽

2003 ◽

Vol 40 (01) ◽

pp. 123-146 ◽

Cited By ~ 1

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.

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Optimal scaling for the transient phase of the random walk Metropolis algorithm: The mean-field limit

The Annals of Applied Probability ◽

10.1214/14-aap1048 ◽

2015 ◽

Vol 25 (4) ◽

pp. 2263-2300 ◽

Cited By ~ 7

Author(s):

Benjamin Jourdain ◽

Tony Lelièvre ◽

Błażej Miasojedow

Keyword(s):

Random Walk ◽

Mean Field ◽

Optimal Scaling ◽

Metropolis Algorithm ◽

Transient Phase ◽

Field Limit ◽

Mean Field Limit ◽

Random Walk Metropolis ◽

The Mean ◽

Random Walk Metropolis Algorithm

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A Metropolis-class sampler for targets with non-convex support

Statistics and Computing ◽

10.1007/s11222-021-10044-4 ◽

2021 ◽

Vol 31 (6) ◽

Author(s):

John Moriarty ◽

Jure Vogrinc ◽

Alessandro Zocca

Keyword(s):

Random Walk ◽

Law Of Large Numbers ◽

Rare Event ◽

General Purpose ◽

Strong Law ◽

Numerical Examples ◽

Large Numbers ◽

Random Walk Metropolis ◽

Improved Performance ◽

Random Walk Metropolis Algorithm

AbstractWe aim to improve upon the exploration of the general-purpose random walk Metropolis algorithm when the target has non-convex support $$A\subset {\mathbb {R}}^d$$ A ⊂ R d , by reusing proposals in $$A^c$$ A c which would otherwise be rejected. The algorithm is Metropolis-class and under standard conditions the chain satisfies a strong law of large numbers and central limit theorem. Theoretical and numerical evidence of improved performance relative to random walk Metropolis are provided. Issues of implementation are discussed and numerical examples, including applications to global optimisation and rare event sampling, are presented.

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