Gibbs Sampling

02 Nov 2024

🚧 Work in progress…

This article will cover Gibbs Sampling, a Markov Chain Monte Carlo (MCMC) algorithm for sampling from complex multivariate probability distributions.

Topics to cover:

• Introduction to Monte Carlo methods
• Markov Chain Monte Carlo (MCMC) basics
• The Gibbs sampling algorithm
• Conditional distributions and full conditionals
• Convergence properties and burn-in
• How Gibbs sampling works: the iterative process
• When to use Gibbs sampling
• Practical examples and applications
• Diagnosing convergence (trace plots, Gelman-Rubin statistic)
• Advantages and limitations
• Comparison with other MCMC methods (Metropolis-Hastings)