Automatic adaptation of MCMC algorithms

TL;DR

This paper presents Auto Adapt MCMC, a novel adaptive algorithm that optimizes MCMC performance through a two-level adaptation process, significantly improving efficiency over existing methods in benchmark tests.

Contribution

Introduction of Auto Adapt MCMC, a two-level adaptive framework that enhances sampler performance and generalizes across standard MCMC algorithms.

Findings

Substantially outperforms existing approaches in efficiency.

Reduces computational time in benchmark problems.

Provides a theoretical foundation for adaptive MCMC.

Abstract

Markov chain Monte Carlo (MCMC) methods are ubiquitous tools for simulation-based inference in many fields but designing and identifying good MCMC samplers is still an open question. This paper introduces a novel MCMC algorithm, namely, Auto Adapt MCMC. For sampling variables or blocks of variables, we use two levels of adaptation where the inner adaptation optimizes the MCMC performance within each sampler, while the outer adaptation explores the valid space of kernels to find the optimal samplers. We provide a theoretical foundation for our approach. To show the generality and usefulness of the approach, we describe a framework using only standard MCMC samplers as candidate samplers and some adaptation schemes for both inner and outer iterations. In several benchmark problems, we show that our proposed approach substantially outperforms other approaches, including an automatic blocking algorithm, in terms of MCMC efficiency and computational time.