Like I said above, I think the multimodality in age_0 is pretty much unavoidable at present: at certain ages, different sources of energy dominate, which can drive atomic transitions in different proportions. There is little additional discriminating power at present that I can incorporate into a prior.
As for the funnel, I have tried a couple approaches… rearranging the third equation above, and express \Gamma in terms of \tau_V \mu and \tau_V (1 - \mu):
\tau_V = \tau_V (1 - \mu) + \tau_V \mu
\Gamma = \frac{0.2 ~ \tau_V}{\xi ~ Z_0 ~ 10^{\log Z}}
In theory, I can also use some related data to get more informative priors on \tau_V \mu, \tau_V (1 - \mu), and \log Q_H (uncertainties at ~.5, .5, and .3 levels, respectively); but for instance, my estimates of \log Q_H are almost certainly overestimates, so correcting them would require another (only weakly-constrained-by-observation) scaling parameter—which is what we were trying to avoid in the first place.
I’ve also tried exploiting some intrinsic structure in my data: we have positional information associated with each set of observations, and present theories suggest that \log Z should vary smoothly with position. So I have defined a GP that governs the positional variation of \log Z, along with the scatter about that mean trend. There is no similar theory for the other parameters, though—and in fact, \log U has recently been shown to have very little spatial correlation at all.
It could be that I am missing something (I will run once again overnight), but none of the above changes seem to be doing me a whole lot of favors (and now it’s much more difficult to debug, since I have to run a large fraction of the data at once). I’ll see what tomorrow brings. Thanks to those of you following along at home 