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Among random sampling methods, Markov Chain Monte Carlo algorithms are foremost. Using a combination of analytical and numerical approaches, we study their convergence properties towards the steady state, within a random walk Metropolis…

Statistical Mechanics · Physics 2024-01-08 Alexei D. Chepelianskii , Satya N. Majumdar , Hendrik Schawe , Emmanuel Trizac

We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuous probability density function. Almost all previous analysis has focused upon continuous…

Probability · Mathematics 2012-10-19 Peter Neal , Gareth Roberts , Wai Kong Yuen

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. In the limit $n\to\infty$, it is well known (see [Ann.…

Probability · Mathematics 2016-08-14 Benjamin Jourdain , Tony Lelièvre , Błażej Miasojedow

The multi-point Metropolis algorithm is an advanced MCMC technique based on drawing several correlated samples at each step and choosing one of them according to some normalized weights. We propose a variation of this technique where the…

Computation · Statistics 2012-10-18 Luca Martino , Victor Pascual Del Olmo , Jesse Read

As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller…

Machine Learning · Computer Science 2016-06-24 Rémi Flamary , Alain Rakotomamonjy , Gilles Gasso

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

An easy-to-implement form of the Metropolis Algorithm is described which, unlike most standard techniques, is well suited to sampling from multi-modal distributions on spaces with moderate numbers of dimensions (order ten) in environments…

High Energy Physics - Phenomenology · Physics 2008-11-26 Benjamin C. Allanach , Christopher G. Lester

Motivated by Bayesian inference with highly informative data we analyze the performance of random walk-like Metropolis-Hastings algorithms for approximate sampling of increasingly concentrating target distributions. We focus on Gaussian…

Computation · Statistics 2022-02-25 Daniel Rudolf , Björn Sprungk

We examine the optimal scaling and the efficiency of the pseudo-marginal random walk Metropolis algorithm using a recently-derived result on the limiting efficiency as the dimension, $d\rightarrow \infty$. We prove that the optimal scaling…

Computation · Statistics 2015-04-24 Chris Sherlock

We present an approach to interface branching random walks with Markov chain Monte Carlo sampling, and to switch seamlessly between the two. The approach is discussed in the context of auxiliary-field quantum Monte Carlo (AFQMC) but is…

Strongly Correlated Electrons · Physics 2023-11-01 Zhi-Yu Xiao , Hao Shi , Shiwei Zhang

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

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

Probability measures supported on submanifolds can be sampled by adding an extra momentum variable to the state of the system, and discretizing the associated Hamiltonian dynamics with some stochastic perturbation in the extra variable. In…

Numerical Analysis · Mathematics 2019-10-15 Tony Lelièvre , Mathias Rousset , Gabriel Stoltz

In this paper we study the ergodicity properties of some adaptive Markov chain Monte Carlo algorithms (MCMC) that have been recently proposed in the literature. We prove that under a set of verifiable conditions, ergodic averages calculated…

Probability · Mathematics 2016-08-16 Christophe Andrieu , Éric Moulines

We show that for any multiple-try Metropolis algorithm, one can always accept the proposal and evaluate the importance weight that is needed to correct for the bias without extra computational cost. This results in a general, convenient,…

Computation · Statistics 2024-10-03 Guanxun Li , Aaron Smith , Quan Zhou

This paper gives sharp rates of convergence for natural versions of the Metropolis algorithm for sampling from the uniform distribution on a convex polytope. The singular proposal distribution, based on a walk moving locally in one of a…

Spectral Theory · Mathematics 2011-04-06 Persi Diaconis , Gilles Lebeau , Laurent Michel

In this paper we examine the implications of the statistical large sample theory for the computational complexity of Bayesian and quasi-Bayesian estimation carried out using Metropolis random walks. Our analysis is motivated by the…

Statistics Theory · Mathematics 2012-01-26 Alexandre Belloni , Victor Chernozhukov

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

We study the integration of functions with respect to an unknown density. We compare the simple Monte Carlo method (which is almost optimal for a certain large class of inputs) and compare it with the Metropolis algorithm (based on a…

Numerical Analysis · Mathematics 2007-06-13 Peter Mathe , Erich Novak

Federated learning performed by a decentralized networks of agents is becoming increasingly important with the prevalence of embedded software on autonomous devices. Bayesian approaches to learning benefit from offering more information as…

Machine Learning · Computer Science 2021-07-16 Vyacheslav Kungurtsev , Adam Cobb , Tara Javidi , Brian Jalaian