  Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful
techniques to sample from almost arbitrary distributions. The flaw in practice
is that it can take a large and/or unknown amount of time to converge to the
stationary distribution. This paper gives sufficient conditions to guarantee
that univariate Gibbs sampling on Markov Random Fields (MRFs) will be fast
mixing, in a precise sense. Further, an algorithm is given to project onto this
set of fast-mixing parameters in the Euclidean norm. Following recent work, we
give an example use of this to project in various divergence measures,
comparing univariate marginals obtained by sampling after projection to common
variational methods and Gibbs sampling on the original parameters.
