Blocked Gibbs sampler

A blocked Gibbs sampler draws groups of coordinates jointly from their full conditional distributions. Each update preserves the joint probability distribution; dependence between blocks can still cause a long mixing time.

On a bipartite image graph, the pixels of one color are conditionally independent given the other color. Draw all black pixels from their independent full conditionals, then draw all whites conditional on the new blacks. Each color update preserves the target law, so their composition does too.