Bayesian inference is often the preferred methodological approach for researchers in genomics, infectious diseases, climate, or financial and industrial models, because it quantifies uncertainty of the statistical reasoning through the posterior probability distributions of such quantities as the model parameters, the missing data, or the predictions. These posterior distributions are explored using MCMC algorithms, such as 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.
Adaptive MCMC is an approach to design self-tuning MCMC algorithms that learn about the target distribution as the sampling progresses and optimise parameters of the sampling algorithm accordingly. They allow for automated and reliable Bayesian inference in these important applications.