Related papers: Metropolis Monte Carlo sampling: convergence, loca…
We study analytically the relaxation eigenmodes of a simple Monte Carlo algorithm, corresponding to a particle in a box which moves by uniform random jumps. Moves outside of the box are rejected. At long times, the system approaches the…
Couplings play a central role in contemporary Markov chain Monte Carlo methods and in the analysis of their convergence to stationarity. In most cases, a coupling must induce relatively fast meeting between chains to ensure good…
Markov chain Monte Carlo methods such as Gibbs sampling and simple forms of the Metropolis algorithm typically move about the distribution being sampled via a random walk. For the complex, high-dimensional distributions commonly encountered…
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…
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…
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.…
We introduce a Monte Carlo algorithm to efficiently compute transport properties of chaotic dynamical systems. Our method exploits the importance sampling technique that favors trajectories in the tail of the distribution of displacements,…
The Monte Carlo within Metropolis (MCwM) algorithm, interpreted as a perturbed Metropolis-Hastings (MH) algorithm, provides an approach for approximate sampling when the target distribution is intractable. Assuming the unperturbed Markov…
Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with…
We study the relaxation of the Metropolis Monte Carlo algorithm corresponding to a single particle trapped in a one-dimensional confining potential, with even jump distributions that ensure that the dynamics verifies detailed balance.…
For a wide class of applications of the Monte Carlo method, we describe a general sampling methodology that is guaranteed to converge to a specified equilibrium distribution function. The method is distinct from that of Metropolis in that…
Metropolis Monte Carlo simulation is a powerful tool for studying the equilibrium properties of matter. In complex condensed-phase systems, however, it is difficult to design Monte Carlo moves with high acceptance probabilities that also…
In recent years, various interacting particle samplers have been developed to sample from complex target distributions, such as those found in Bayesian inverse problems. These samplers are motivated by the mean-field limit perspective and…
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…
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…
The Metropolis implementation of the Monte Carlo algorithm has been developed to study the equilibrium thermodynamics of many-body systems. Choosing small trial moves, the trajectories obtained applying this algorithm agree with those…
Markov chain Monte Carlo methods have become standard tools in statistics to sample from complex probability measures. Many available techniques rely on discrete-time reversible Markov chains whose transition kernels build up over the…
The Metropolis-Hastings algorithm has been extensively studied in the estimation and simulation literature, with most prior work focusing on convergence behavior and asymptotic theory. However, its covariance structure-an important…
Hamiltonian Monte Carlo (HMC) is a state-of-the-art Markov chain Monte Carlo sampling algorithm for drawing samples from smooth probability densities over continuous spaces. We study the variant most widely used in practice, Metropolized…
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…