Data analysis recipes: Using Markov Chain Monte Carlo

TL;DR

This paper provides a pedagogical overview of Markov Chain Monte Carlo methods, offering practical advice on their application, convergence testing, and effective use in probabilistic inference tasks.

Contribution

It introduces practical guidelines for using MCMC in real inference problems, emphasizing autocorrelation time and sampling for integrals.

Findings

Autocorrelation time is crucial for convergence assessment.

Proper tuning and initialization improve MCMC efficiency.

MCMC is best used for integral estimation and uncertainty quantification.

Abstract

Markov Chain Monte Carlo (MCMC) methods for sampling probability density functions (combined with abundant computational resources) have transformed the sciences, especially in performing probabilistic inferences, or fitting models to data. In this primarily pedagogical contribution, we give a brief overview of the most basic MCMC method and some practical advice for the use of MCMC in real inference problems. We give advice on method choice, tuning for performance, methods for initialization, tests of convergence, troubleshooting, and use of the chain output to produce or report parameter estimates with associated uncertainties. We argue that autocorrelation time is the most important test for convergence, as it directly connects to the uncertainty on the sampling estimate of any quantity of interest. We emphasize that sampling is a method for doing integrals; this guides our thinking about how MCMC output is best used.