Ergonomic and Reliable Bayesian Inference with Adaptive Markov Chain Monte Carlo

Abstract

Adaptive Markov chain Monte Carlo (MCMC) methods provide an ergonomic way to perform Bayesian inference, imposing mild modeling constraints and requiring little user specification. The aim of this section is to provide a practical introduction to selected set of adaptive MCMC methods and to suggest guidelines for choosing appropriate methods for certain classes of models. We consider simple unimodal targets with random-walk-based methods, multimodal target distributions with parallel tempering, and Bayesian hidden Markov models using particle MCMC. The section is complemented by an easy-to-use open-source implementation of the presented methods in Julia, with examples.