Posterior-based proposals for speeding up Markov chain Monte Carlo

TL;DR

This paper introduces posterior-based proposals (PBPs), a new MCMC update method that improves sampling efficiency across various complex models by enabling large joint updates with high acceptance rates, often outperforming existing methods.

Contribution

The paper presents PBPs, a novel and general MCMC update technique applicable to many models with directed acyclic graph structures, significantly enhancing sampling speed and efficiency.

Findings

PBPs achieve higher or comparable speed to state-of-the-art methods.

PBPs maintain good acceptance rates (~33%).

PBPs outperform other approaches by up to a factor of 10 in diverse models.

Abstract

Markov chain Monte Carlo (MCMC) is widely used for Bayesian inference in models of complex systems. Performance, however, is often unsatisfactory in models with many latent variables due to so-called poor mixing, necessitating development of application specific implementations. This paper introduces "posterior-based proposals" (PBPs), a new type of MCMC update applicable to a huge class of statistical models (whose conditional dependence structures are represented by directed acyclic graphs). PBPs generates large joint updates in parameter and latent variable space, whilst retaining good acceptance rates (typically 33%). Evaluation against other approaches (from standard Gibbs / random walk updates to state-of-the-art Hamiltonian and particle MCMC methods) was carried out for widely varying model types: an individual-based model for disease diagnostic test data, a financial stochastic volatility model, a mixed model used in statistical genetics and a population model used in ecology. Whilst different methods worked better or worse in different scenarios, PBPs were found to be either near to the fastest or significantly faster than the next best approach (by up to a factor of 10). PBPs therefore represent an additional general purpose technique that can be usefully applied in a wide variety of contexts.