meeting 2025 02 27 n315 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

Wrapping up some of the discussion from yesterday on the uncertainties/spectra/chi2's. Note I've also replaced the Overleaf kinematics with a symmetric y-axis, too.

One thing we wanted to check out was a map of the unceratinties on the kinematics as a function of position on the sky. I've made that plot below, but I don't see anything too suspicious looking from this plot other than the uncertainties are tiny (as we already know).

Errors on the Sky
images/250227/testing_uncertainties-1.png

I've refit the spectra using the same settings from the original reduction, and in the process I found a stupid mistake in my work that could potentially be contributing to our uncertainty issue and thus our chi2 weirdness.
- Specifically, when I was fitting the kinematics ~a year ago, we were still experimenting with the optimal settings to be used for the reduction, so I had been only using 10 Monte Carlo realizations rather than 100 realiaztions to speed up the processing time. When we settled on a final set of kinematics, I hadn't gone back to rerun our spectral fits with all 100 Monte Carlo realizations, so our values and uncertainties were coming only from 10 MC realizations instead of 100.
- The long story short is that I can reproduce our kinematics essentially perfectly using nMc=10, but the uncertainty distribution is slightly different than the uncertainty distribution from 100 Mc realizations, and I suspect this might be impacting our final chi2.
  - This also slightly changes the kinematics, since our kinematics are the median across the MC realizations. One upshot is that the non-perturbed spectral kinematics across both the nMc=10 and nMc=100 realizations are identical, as are the actual spectral fits.

And here are some diagnostics showing what is described above: First, here's my reproduction of our current kinematics. Again, the key here is that these only use 10 MC realizations to compute the uncertainties and the median values. At this level, the two sets of kinematics are strongly consistent with one another.
- Again, it's important to note that the fiducial, unperturbed fits to these spectra are identical to one another, and the offset between the nMc=10 and nMc=100 case is only due to us taking a median over the 10 vs. 100 realizations.
- I've got both the reproduced and the original kinematics here to show their means and distributions are virtually identical.

Original vs. nMc = 10 Repro	Original vs. nMc = 100 Repro
[images/250227/original_vs_reproduction_nmc10.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250227/original_vs_reproduction.png)

And here's the histogram of errors derived using nMc = 10 (our current values) vs. nMc = 100 (what I should have been using all along). The nMc = 10 errors in particular have a much wider distrubtion but overall have very similar means, so I think this is why certain bins are contributing greatly to the chi2 (their uncertainties are on the small side of the distribution).

Histograms of nMc=10 (reproduced) vs. nMc=100 errors	Histograms of nMc=10 (original) vs. nMc=100 errors
[images/250227/errors.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250227/errors_orig.png)

So where do we go from here:
- On one hand, because the actual fiducial fits are identical between the two (that is to say, the fits to the raw spectra, not the median over the perturbed spectra), I'm inclined to keep our kinematics as they are an re-assign their errors based on the nMc=100 case, and then recompute our galaxy parameters and such.
- On the other hand, because our kinematics are not the fiducial fits but rather medians over the MC iterations, it feels a bit off to simply reassign the errors, but then we run the risk of changing the kinematics we've been using up to now.
- All in all, I'm very sorry for not catching this sooner, and apologies for the wrench being thrown into our analysis here at the last minute.

Putting up some plots here following our email exchange. Here are the heatmaps showing the chi2 using the nMc=10 vs. the nMc=100 errors for both the full dataset and summed for each moment at the bottom.
h6 is noticeably improved and is no longer the dominant contribution to the chi2.

	nMC=10 Errors	nMC=100 Errors
Full GMOS Dataset	[images/250226/gmos_kinem.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250227/gmos_kinem_changed_errors.png)
For each GMOS moment	[images/250226/gmos_kinem_moments.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250227/gmos_kinem_moments_changed_errors.png)