We are doing MCMC sampling over an n-dimensional space with a population of MCMCs. The goal is to have them stop when they approximately converge. The problem is that the convergence, which is so easily visually seen is hard to code. Typical Gelman-Rubin/Geweke work well for well behaved functions, but for some nasty ones with weird features, they oscillate or have random peaks that do not indicate the steady slow convergence as wanted.
What other convergence statistics can you recommend? I was looking at using time series methods but cannot find any papers on time series convergence.
I was thinking would it be possible to take a discrete fourier and do something with that or.....?
Some already looked at: Cramer von Mises, Kolmogorov-Smirnov, Kuiper, Raftley-Lewis, Heinberg-Wurtley.