Variance Reduction for Metropolis-Hastings Samplers

by   Angelos Alexopoulos, et al.
University of Cambridge

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 post-process manner utilising all proposal values of the Metropolis algorithms. Variance reduction is achieved by producing control variates through the approximate solution of the Poisson equation associated with the target density of the Markov chain. The proposed method is based on approximating the target density with a Gaussian and then utilising accurate solutions of the Poisson equation for the Gaussian case. This leads to an estimator that uses two key elements: (i) a control variate from the Poisson equation that contains an intractable expectation under the proposal distribution, (ii) a second control variate to reduce the variance of a Monte Carlo estimate of this latter intractable expectation. Simulated data examples are used to illustrate the impressive variance reduction achieved in the Gaussian target case and the corresponding effect when target Gaussianity assumption is violated. Real data examples on Bayesian logistic regression and stochastic volatility models verify that considerable variance reduction is achieved with negligible extra computational cost.


page 1

page 2

page 3

page 4


Solving the Poisson equation using coupled Markov chains

This article draws connections between unbiased estimators constructed f...

Diffusion approximations and control variates for MCMC

A new methodology is presented for the construction of control variates ...

Randomized Dimension Reduction for Monte Carlo Simulations

We present a new unbiased algorithm that estimates the expected value of...

Multilevel Surrogate-based Control Variates

Monte Carlo (MC) sampling is a popular method for estimating the statist...

Regularised Zero-Variance Control Variates for High-Dimensional Variance Reduction

Zero-variance control variates (ZV-CV) are a post-processing method to r...

Approximate Inference for Nonstationary Heteroscedastic Gaussian process Regression

This paper presents a novel approach for approximate integration over th...

Regularised Zero-Variance Control Variates

Zero-variance control variates (ZV-CV) is a post-processing method to re...

Please sign up or login with your details

Forgot password? Click here to reset