Gibbs Sampling
Gibbs sampling is a special case of Metropolis-Hastings: it samples each coordinate from its conditional distribution p(x_i|x_{-i}), needs no accept-reject step, and suits high-dimensional distributions.
Purpose
To provide a simple MCMC sampling method for high-dimensional joint distributions without tuning a proposal distribution.
Mechanism
Iterate over each dimension i, sampling from the conditional p(x_i | current values of the other dimensions). Conditional distributions are usually easier to sample than the joint. Convergence requires the conditionals to cover the target distribution sufficiently.
Use cases
- Bayesian network inference
- High-dimensional sampling
- Image segmentation