I think I have some problem that I do not understand well. Probably I have to study more but I just put it here so maybe I can understand.
Basically I did a cosmological analysis with n parameters (3 for LCDM, + 2 extra) with my likelihood plus bao, and everything was good. The mean (weighted) value of the parameters from the run gave me a good fit for the data.
Then I run a cosmological analysis with n+1 parameters (3+1 for LCDM, + 2 extra). Now the mean value of the parameters gives me a very bad fit, in the sense that the fit is way off the data (--> bad chi2, but the mean chi2 is fine).
Maybe it was something wrong with the code, so I try the minimizer. I obtain a very good fit.
So it seems that varying that one extra parameter makes things crazy. It is like one of the cases in which the mean is different from the maximum a posteriori (if you have something different from gaussian for example or if you have some surface as your posterior and the mean lies outside your surface). For some marginalized parameters the 1d marginalized posterior does not seem gaussian but it is a 'weak' non gaussianity (in the sense of asymmetry).
Probably I still have to understand things better, but does any one has some intuition? Could it be that I have some wrong proposal matrix and the sampler it is not exploring well the space? (I tried to start from different positions but it seems I always end up in the wrong place, also from what I understood setting learn proposal to true should solve the problem for finding a perfect proposal matrix.)
Theoretically speaking, could something like this happen? (because maybe it is just a bug/conceptual error I am not seeing)
Do you have best practices to debug mcmc?
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