Reversible Jump Monte Carlo for gaussian mixtures
I want to determine the correct number of gaussian's to approximate a physical spectrum.
I am therefore trying to implement the Reversible Jump Monte Carlo algorithm for gaussian mixtures as outlined in this paper:
Richardson and Green 1997 (JSTOR: An Error Occurred Setting Your User Cookie).
This algorithm is rather complicated to implement (I think), and therefore I'd like to do some tests to make sure I've implemented it correctly. I am only using normal MCMC moves for the parameters and split/merge moves for the trans-dimensional moves (ie. no birth/death moves at this point). As a starting point, I am using a uniform prior for all the parameters as well as the number of lines (as opposed to what Richardson and Green have). Also if I set the likelihood to 1 (ie. remove any information from data), it seems I should get back just the uniform prior for the parameters and number of lines.
However, I do not get a uniform prior... Should I? Is this even a sensible test of the algorithm? What else could I check? It seems to me that I get more splits than merges and so the system hangs around at Nmax most of the time, where Nmax is the maximum number of gaussians I allow.