Resampling from the past to improve on MCMC algorithms

TL;DR

This paper proposes a resampling technique from past observations in MCMC algorithms to accelerate convergence without affecting the target distribution, demonstrated through Bayesian models in finance and phylogeny.

Contribution

It introduces a theoretically justified resampling method from past states in MCMC, enhancing convergence speed while preserving the limit distribution.

Findings

Resampling from the past accelerates MCMC convergence.

Proper resampling does not alter the target distribution.

Demonstrated effectiveness on Bayesian stochastic volatility and phylogeny models.

Abstract

We introduce the idea that resampling from past observations in a Markov Chain Monte Carlo sampler can fasten convergence. We prove that proper resampling from the past does not disturb the limit distribution of the algorithm. We illustrate the method with two examples. The first on a Bayesian analysis of stochastic volatility models and the other on Bayesian phylogeny reconstruction.