# What is the state-of-the-art regarding sampling from discrete distribution?

After struggling with auto-Poisson model (a.k.a. Random Markov Network with conditional Poisson distributions) trying to force Gibbs sampler to obtain discrete sample of the network (since I know conditional distributions) I realized that I have never seen discrete version of this sampler.

I wonder what is the state-of-the-art regarding sampling from discrete distribution (not confined to Bayesian posterior sampling)? Is there something like Gibbs sampler to sample from conditional discrete distributions?

• Gibbs sampling can be used for discrete distributions as well, under appropriate considerations. This in mentioned, for instance, in the wikipedia entry, "Implementation" section. – user10525 Jul 24 '12 at 12:22

This is a very puzzling question: the Gibbs sampler draws its name from Gibbs random fields where it was originally used by the Geman brothers to generate realisations from such discrete models. For instance the Ising model is made of a vector of random variables each taking values in $\{-1,1\}$...