Comment by tansey

Stan (http://mc-stan.org/documentation/) is arguably the most advanced language. It's especially pushing the bounds of doing automatic variational inference, for the scenario where your model does not have a nice conjugate form that would be amenable to Gibbs sampling. It's not quite reached what I would say is production-quality, but some of the best people in the world of computational Bayesian methods (e.g., Michael Betancourt, most of David Blei's lab, etc.) are working on it.