After asking a question about Gibbs sampling earlier, I have another one for you.
I have not been able to find laymen's background on this, the only referenced use I've found for this is in statistical papers (Roberts et al. 2003, Gelfand et al. 1995), to name a few.
In an apparent try to speed up the convergence of Gibbs sampling, we might try a re-paramatrization of the parameters of interest. This is in order to make them less dependent on one another, as I understand it. Because, the less dependent, the faster the convergence.
The two different parametrization have been termed 'ancillary' and 'sufficient', or alternatively 'non-centered' and 'centered'. These were introduced to me in a fairly specific example, and I would therefore very much appreciate it if someone can introduce these concepts more generally (i.e., how is an ancillary parametrization different from a sufficient one). In my case, the sufficient parametrization is faster - is the sufficient parametrization always ideal?