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Delayed-acceptance Metropolis-Hastings and delayed-acceptance pseudo-marginal Metropolis-Hastings algorithms can be applied when it is computationally expensive to calculate the true posterior or an unbiased stochastic approximation…

Statistics Theory · Mathematics 2021-02-24 Chris Sherlock , Alexandre Thiery , Andrew Golightly

One main limitation of the existing optimal scaling results for Metropolis--Hastings algorithms is that the assumptions on the target distribution are unrealistic. In this paper, we consider optimal scaling of random-walk Metropolis…

Computation · Statistics 2020-05-05 Jun Yang , Gareth O. Roberts , Jeffrey S. Rosenthal

Convergence rate analyses of random walk Metropolis-Hastings Markov chains on general state spaces have largely focused on establishing sufficient conditions for geometric ergodicity or on analysis of mixing times. Geometric ergodicity is a…

Statistics Theory · Mathematics 2023-07-24 Riddhiman Bhattacharya , Galin L. Jones

Pseudo-marginal Markov chain Monte Carlo methods for sampling from intractable distributions have gained recent interest and have been theoretically studied in considerable depth. Their main appeal is that they are exact, in the sense that…

Computation · Statistics 2015-03-25 Felipe J. Medina-Aguayo , Anthony Lee , Gareth O. Roberts

This paper proposes a new sampling scheme based on Langevin dynamics that is applicable within pseudo-marginal and particle Markov chain Monte Carlo algorithms. We investigate this algorithm's theoretical properties under standard…

Methodology · Statistics 2016-05-30 Christopher Nemeth , Chris Sherlock , Paul Fearnhead

In this paper we shall consider optimal scaling problems for high-dimensional Metropolis--Hastings algorithms where updates can be chosen to be lower dimensional than the target density itself. We find that the optimal scaling rule for the…

Probability · Mathematics 2007-05-23 Peter Neal , Gareth Roberts

There has been a recent surge of interest in coupling methods for Markov chain Monte Carlo algorithms: they facilitate convergence quantification and unbiased estimation, while exploiting embarrassingly parallel computing capabilities.…

Computation · Statistics 2025-09-03 Tamás P. Papp , Chris Sherlock

We consider the Random Walk Metropolis algorithm on $\mathbb{R}^n$ with Gaussian proposals, and when the target probability measure is the $n$-fold product of a one-dimensional law. It is well known (see Roberts et al. (Ann. Appl. Probab. 7…

Methodology · Statistics 2014-10-22 Benjamin Jourdain , Tony Lelièvre , Błażej Miasojedow

The performance of Metropolis-Hastings algorithms is highly sensitive to the choice of step size, and miss-specification can lead to severe loss of efficiency. We study algorithms with randomized step sizes, considering both…

Computation · Statistics 2026-01-28 Sebastiano Grazzi , Samuel Livingstone , Lionel Riou-Durand

For sufficiently smooth targets of product form it is known that the variance of a single coordinate of the proposal in RWM (Random walk Metropolis) and MALA (Metropolis adjusted Langevin algorithm) should optimally scale as $n^{-1}$ and as…

Probability · Mathematics 2020-07-15 Jure Vogrinc , Wilfrid Stephen Kendall

We propose an adaptive independent Metropolis--Hastings algorithm with the ability to learn from all previous proposals in the chain except the current location. It is an extension of the independent Metropolis--Hastings algorithm.…

Probability · Mathematics 2009-03-04 Lars Holden , Ragnar Hauge , Marit Holden

In this paper, we shall optimize the efficiency of Metropolis algorithms for multidimensional target distributions with scaling terms possibly depending on the dimension. We propose a method for determining the appropriate form for the…

Probability · Mathematics 2007-10-25 Mylène Bédard

We propose an adaptive Metropolis-Hastings algorithm in which sampled data are used to update the proposal distribution. We use the samples found by the algorithm at a particular step to form the information-theoretically optimal mean-field…

Other Condensed Matter · Physics 2007-05-23 David H. Wolpert , Chiu Fan Lee

We examine challenges to sampling from Boltzmann distributions associated with multiscale energy landscapes. The multiscale features, or "roughness," corresponds to highly oscillatory, but bounded, perturbations of a smooth landscape.…

Numerical Analysis · Mathematics 2020-07-02 Petr Plecháč , Gideon Simpson

The Random Walk Metropolis (RWM) algorithm is a Metropolis- Hastings MCMC algorithm designed to sample from a given target distribution \pi with Lebesgue density on R^N. RWM constructs a Markov chain by randomly proposing a new position…

Probability · Mathematics 2016-08-31 J. Kuntz , M. Ottobre , A. M. Stuart

We investigate local MCMC algorithms, namely the random-walk Metropolis and the Langevin algorithms, and identify the optimal choice of the local step-size as a function of the dimension $n$ of the state space, asymptotically as…

Probability · Mathematics 2009-08-07 Alexandros Beskos , Gareth Roberts , Andrew Stuart

I show how one can modify the random-walk Metropolis MCMC method in such a way that a sequence of modified Metropolis updates takes little computation time when the rejection rate is outside a desired interval. This allows one to…

Statistics Theory · Mathematics 2007-06-13 Radford M. Neal

This work extends Roberts et al. (1997) by considering limits of Random Walk Metropolis (RWM) applied to block IID target distributions, with corresponding block-independent proposals. The extension verifies the robustness of the optimal…

Probability · Mathematics 2019-02-19 Jeffrey Negrea

The choice of the increment distribution is crucial for the random-walk Metropolis-Hastings (RWM) algorithm. In this paper we study the optimal choice in high-dimension setting among all possible increment distributions. The conclusion is…

Methodology · Statistics 2016-05-24 Kengo Kamatani

We study the Ergodic Properties of Random Walks in stationary ergodic environments without uniform ellipticity under a minimal assumption. There are two main components in our work. The first step is to adopt the arguments of Lawler to…

Probability · Mathematics 2026-02-03 Ayan Ghosh