Related papers: Diffusion approximations and control variates for …

In this paper, we propose a variance reduction approach for Markov chains based on additive control variates and the minimization of an appropriate estimate for the asymptotic variance. We focus on the particular case when control variates…

In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A…

A general methodology is introduced for the construction and effective application of control variates to estimation problems involving data from reversible MCMC samplers. We propose the use of a specific class of functions as control…

We introduce a general framework that constructs estimators with reduced variance for random walk Metropolis and Metropolis-adjusted Langevin algorithms. The resulting estimators require negligible computational cost and are derived in a…

A general methodology is presented for the construction and effective use of control variates for reversible MCMC samplers. The values of the coefficients of the optimal linear combination of the control variates are computed, and adaptive,…

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…

In statistics and machine learning, approximation of an intractable integration is often achieved by using the unbiased Monte Carlo estimator, but the variances of the estimation are generally high in many applications. Control variates…

Two popular classes of methods for approximate inference are Markov chain Monte Carlo (MCMC) and variational inference. MCMC tends to be accurate if run for a long enough time, while variational inference tends to give better approximations…

Many popular statistical models for complex phenomena are intractable, in the sense that the likelihood function cannot easily be evaluated. Bayesian estimation in this setting remains challenging, with a lack of computational methodology…

Calculating averages with respect to multimodal probability distributions is often necessary in applications. Markov chain Monte Carlo (MCMC) methods to this end, which are based on time averages along a realization of a Markov process…

We consider the efficient use of an approximation within Markov chain Monte Carlo (MCMC), with subsequent importance sampling (IS) correction of the Markov chain inexact output, leading to asymptotically exact inference. We detail…

In this paper we study the asymptotic behavior of the Random-Walk Metropolis algorithm on probability densities with two different `scales', where most of the probability mass is distributed along certain key directions with the…

We study control variate methods for Markov chain Monte Carlo (MCMC) in the setting of deterministic sweep sampling using $K\geq 2$ transition kernels. New variance reduction results are provided for MCMC averages based on sweeps over…

Adaptive Markov Chain Monte Carlo (AMCMC) is a class of MCMC algorithms where the proposal distribution changes at every iteration of the chain. In this case it is important to verify that such a Markov Chain indeed has a stationary…

In this article we consider Bayesian estimation of static parameters for a class of partially observed McKean-Vlasov diffusion processes with discrete-time observations over a fixed time interval. This problem features several obstacles to…

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…

In this paper we examine a control variate estimator for a quantity that can be expressed as the expectation of a functional of a random process, that is itself the solution of a differential equation driven by fast mean-reverting ergodic…

We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC) algorithms to the Computer Science notion of algorithm complexity. Our main result states that any diffusion limit of a Markov process implies a…

Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected value of a function with respect to a, possibly unnormalized, probability distribution. A general purpose variance reduction technique for the MCMC…

Various Markov chain Monte Carlo (MCMC) methods are studied to improve upon random walk Metropolis sampling, for simulation from complex distributions. Examples include Metropolis-adjusted Langevin algorithms, Hamiltonian Monte Carlo, and…