Adaptive MCMC

Explaining the science

Bayesian inference is often the preferred methodological approach for researchers in modelling genomics, infectious diseases, climate, financial markets, and many others. It provides a way of combining new evidence with prior beliefs – after observing some evidence, the resulting output or ‘posterior distribution’ of a model can then be treated as an input or ‘prior distribution’, and a new posterior distribution can be computed from new evidence, and so on.

These posterior distributions are often explored using Markov chain Monte Carlo (MCMC) algorithms. Monte Carlo methods are a broad class of computational algorithms that rely on repeated, random sampling to obtain numerical results. Markov chains are algorithms used for working with a series of events (for example a system being in particular states) to predict the possibility of a certain event based on what other events have happened. Used in conjunction, MCMC methods approximate the posterior distribution of a parameter of interest through random sampling.

MCMC methods include the Metropolis-Hastings, the Metropolis Adjusted Langevin algorithm, the Gibbs sampler, Hybrid Monte Carlo, or the slice sampler. However, in modern high-dimensional applications, off the shelf versions of these algorithms often need extensive tuning for optimised performance, that are time consuming and require expert knowledge.