Marginal MCMC: The tool to solve our statistical computing problems?

I recently became aware of two papers by David van Dyk on a new approach to Gibbs sampling using incompatible conditional distributions. This seems similar to the parameter expansion or redundant parameter idea developed by C. Liu, J. Liu, Meng, Rubin, van Dyk, and others, but perhaps a bit more generalizable and thus usable in routine problems.

Here’s the theoretical paper (with Taeyoung Park).

And here’s the more applied paper (which has a logistic regression example), with Hosung Kang.

This looks great, although I’m still not sure exactly how to apply this to our problems. Maybe we’re getting closer, though…