The Metropolis-Hastings algorithm

TL;DR

This paper provides a clear, self-contained introduction to the Metropolis-Hastings algorithm, illustrating its principles with examples and R code, and discusses recent extensions of the method.

Contribution

It offers a foundational overview of the Metropolis-Hastings algorithm with practical examples and references to recent advancements.

Findings

Demonstrates the algorithm with simple examples

Provides R code for implementation

Discusses recent extensions of the method

Abstract

This short note is a self-contained and basic introduction to the Metropolis-Hastings algorithm, this ubiquitous tool used for producing dependent simulations from an arbitrary distribution. The document illustrates the principles of the methodology on simple examples with R codes and provides references to the recent extensions of the method.