Improving the Asymptotic Performance of Markov Chain Monte-Carlo by Inserting Vortices

Abstract

We present a new way of converting a reversible finite Markov chain into a non-reversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversible chain is reduced. The method is applicable to any reversible chain whose states are not connected through a tree, and can be interpreted graphically as inserting vortices into the state transition graph. Our result confirms that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.

Published in NIPS 2010

References in corpus (1)

• Improving Asymptotic Variance of MCMC Estimators: Non-reversible Chains are Better

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• Acceleration of convergence to equilibrium in Markov chains by breaking detailed balance
• Metropolis-Hastings reversiblizations of non-reversible Markov chains
• A general perspective on the Metropolis-Hastings kernel
• Non-reversible Markov chain Monte Carlo for sampling of districting maps
• Estimating the Mixing Time of Ergodic Markov Chains
• Non-reversible, tuning- and rejection-free Markov chain Monte Carlo via iterated random functions
• Analysis of high-dimensional Continuous Time Markov Chains using the Local Bouncy Particle Sampler
• Variational Formulas of Asymptotic Variance for General Discrete-time Markov Chains
• Bounds on Lifting Continuous Markov Chains to Speed Up Mixing
• Accelerating MCMC Algorithms