Metropolis-Hastings Algorithm

02 Nov 2024

🚧 Work in progress…

This article will cover the Metropolis-Hastings algorithm, a foundational Markov Chain Monte Carlo (MCMC) method for sampling from probability distributions.

Topics to cover:

• Historical context and motivation
• The Metropolis algorithm (original version)
• The Metropolis-Hastings generalization
• Proposal distributions and their role
• Acceptance ratio and the acceptance-rejection step
• Detailed balance and reversibility
• Convergence to the target distribution
• Practical implementation
• Choosing good proposal distributions
• Applications in Bayesian inference
• Tuning the algorithm (acceptance rates)
• Comparison with Gibbs sampling
• Random walk vs. independence samplers