Related papers: Optimal scaling of the Random Walk Metropolis algo…
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…
In this work, we propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our…
We prove a general result that if a Metropolis--Hastings algorithm has a proposal that is not geometrically ergodic and the acceptance rate approaches unity at a suitable rate as the state variable becomes large, then the Metropolised chain…
In this paper, we prove large deviation principles for the empirical measures associated with the Independent Metropolis Hastings (IMH) sampler and the Metropolis-adjusted Langevin Algorithm (MALA). These are the first large deviation…
We introduce new Gaussian proposals to improve the efficiency of the standard Hastings-Metropolis algorithm in Markov chain Monte Carlo (MCMC) methods, used for the sampling from a target distribution in large dimension $d$. The improved…
We provide a clarification of the description of Langevin diffusions on Riemannian manifolds and of the measure underlying the invariant density. As a result we propose a new position-dependent Metropolis-adjusted Langevin algorithm (MALA)…
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…
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.…
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…
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…
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…
In this study, we investigate the performance of the Metropolis-adjusted Langevin algorithm in a setting with constraints on the support of the target distribution. We provide a rigorous analysis of the resulting Markov chain, establishing…
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…
Optimal scaling has been well studied for Metropolis-Hastings (M-H) algorithms in continuous spaces, but a similar understanding has been lacking in discrete spaces. Recently, a family of locally balanced proposals (LBP) for discrete spaces…
This paper introduces a new Markov Chain Monte Carlo method for Bayesian variable selection in high dimensional settings. The algorithm is a Hastings-Metropolis sampler with a proposal mechanism which combines a Metropolis Adjusted Langevin…
The Langevin Markov chain algorithms are widely deployed methods to sample from distributions in challenging high-dimensional and non-convex statistics and machine learning applications. Despite this, current bounds for the Langevin…
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…
We derive the first explicit bounds for the spectral gap of a random walk Metropolis algorithm on $R^d$ for any value of the proposal variance, which when scaled appropriately recovers the correct $d^{-1}$ dependence on dimension for…
We study the scaling laws of diffusion in two-dimensional media with long-range correlated disorder through exact enumeration of random walks. The disordered medium is modelled by percolation clusters with correlations decaying with the…
In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…