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Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target…

Probability · Mathematics 2012-10-05 Jonathan C. Mattingly , Natesh S. Pillai , Andrew M. Stuart

We present explicit methods for simulating diffusions whose generator is self-adjoint with respect to a known (but possibly not normalizable) density. These methods exploit this property and combine an optimized Runge-Kutta algorithm with a…

Numerical Analysis · Mathematics 2014-06-27 Nawaf Bou-Rabee , Aleksandar Donev , Eric Vanden-Eijnden

The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm that incorporates the gradient of the logarithm of the target density in its proposal distribution. In an earlier joint work \citet{pill:stu:12}, the author had…

Computation · Statistics 2025-01-15 Natesh S. Pillai

The popularity of Adaptive MCMC has been fueled on the one hand by its success in applications, and on the other hand, by mathematically appealing and computationally straightforward optimisation criteria for the Metropolis algorithm…

Computation · Statistics 2018-01-30 Cyril Chimisov , Krzysztof Latuszynski , Gareth Roberts

We consider versions of the Metropolis algorithm which avoid the inefficiency of rejections. We first illustrate that a natural Uniform Selection Algorithm might not converge to the correct distribution. We then analyse the use of Markov…

Statistics Theory · Mathematics 2024-04-04 J. S. Rosenthal , A. Dote , K. Dabiri , H. Tamura , S. Chen , A. Sheikholeslami

Our article deals with Bayesian inference for a general state space model with the simulated likelihood computed by the particle filter. We show empirically that the partially or fully adapted particle filters can be much more efficient…

Methodology · Statistics 2010-06-11 Michael Pitt , Ralph Silva , Paolo Giordani , Robert Kohn

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

We present an adaptive method for the automatic scaling of Random-Walk Metropolis-Hastings algorithms, which quickly and robustly identifies the scaling factor that yields a specified overall sampler acceptance probability. Our method…

Methodology · Statistics 2010-06-21 P. H. Garthwaite , Y. Fan , S. A. Sisson

The Metropolis algorithm involves producing a Markov chain to converge to a specified target density $\pi$. In order to improve its efficiency, we can use the Rejection-Free version of the Metropolis algorithm, which avoids the inefficiency…

Computation · Statistics 2022-10-20 Sigeng Chen , Jeffrey S. Rosenthal , Aki Dote , Hirotaka Tamura , Ali Sheikholeslami

The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance…

Computation · Statistics 2025-09-30 Sarra Abaoubida , Mylène Bédard , Florian Maire

There are two ways of speeding up MCMC algorithms: (1) construct more complex samplers that use gradient and higher order information about the target and (2) design a control variate to reduce the asymptotic variance. While the efficiency…

Probability · Mathematics 2019-06-19 Aleksandar Mijatović , Jure Vogrinc

This work is driven by the ubiquitous dissent over the abilities and contributions of the Metropolis-Hastings and reversible jump algorithm within the context of trans dimensional sampling. We demystify this topic by taking a deeper look…

Statistics Theory · Mathematics 2019-08-05 Tobias Siems , Lisa Koeppel

Very recently, Transformation based Markov Chain Monte Carlo (TMCMC) was proposed by Dutta and Bhattcharya (2013) as a much efficient alternative to the Metropolis-Hastings algorithm, Random Walk Metropolis (RWM) algorithm, especially in…

Computation · Statistics 2017-07-26 Kushal Kr Dey , Sourabh Bhattacharya

It is well known in many settings that reversible Langevin diffusions in confining potentials converge to equilibrium exponentially fast. Adding irreversible perturbations to the drift of a Langevin diffusion that maintain the same…

Methodology · Statistics 2019-07-02 Michela Ottobre , Natesh S. Pillai , Konstantinos Spiliopoulos

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

This work develops a powerful and versatile framework for determining acceptance ratios in Metropolis-Hastings type Markov kernels widely used in statistical sampling problems. Our approach allows us to derive new classes of kernels which…

Statistics Theory · Mathematics 2021-07-21 Nathan E. Glatt-Holtz , Justin A. Krometis , Cecilia F. Mondaini

We analyse computational efficiency of Metropolis-Hastings algorithms with stochastic AR(1) process proposals. These proposals include, as a subclass, discretized Langevin diffusion (e.g. MALA) and discretized Hamiltonian dynamics (e.g.…

Computation · Statistics 2016-05-23 Richard A. Norton , Colin Fox

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

The Metropolis-within-Gibbs (MwG) algorithm is a widely used Markov Chain Monte Carlo method for sampling from high-dimensional distributions when exact conditional sampling is intractable. We study MwG with Random Walk Metropolis (RWM)…

Machine Learning · Statistics 2025-10-01 Cecilia Secchi , Giacomo Zanella

We consider the problem of sampling from a strongly log-concave density in $\mathbb{R}^d$, and prove a non-asymptotic upper bound on the mixing time of the Metropolis-adjusted Langevin algorithm (MALA). The method draws samples by…

Machine Learning · Statistics 2019-12-12 Raaz Dwivedi , Yuansi Chen , Martin J. Wainwright , Bin Yu