meeting 2024 11 07 n315 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

A few follow ups from the most recent meeting, mostly exploring the robustness of the fits vs K and nu and the convergence on the final sets of parameters. I've also got a few jacknife tests. Still have some work in progress but wanted to get this on Github before the weekend/as I move stuff back to Overleaf.
Robustness of the fits:
- I've run a finer grid vs. K for both nu = 0.5 and nu = 1.5, and have them plotted in a vertical style plot.
- As we saw before, there's a strange feature in the M/L panel which happens in the range of K=70 to K=90 or so, where the M/L preference gets slightly increased (which is covariant with the dark matter halo). Strangely, this "bump" disappears for lower and higher K.
- The nu=0.5 and nu=1.5 parameters are very similar to one another, but the nu=0.5 posteriors are, on the whole, much tighter than the nu = 1.5 case. I believe that the nu = 1.5 posteriors entirely encompass the nu=0.5 posteriors in all cases. While there might be a very small discrepency between fits, I think things at this stage are largely consistent/I'm not too pressed about any differences we see here.
Jacknife tests:
- I ran a set of jacknife tests for K = 60, K = 80, and K = 100, both nu = 0.5 and nu = 1.5. I chose these K's since this seems to get around the K = 80 bump on both sides, but also keeping the K=80 case to see if there is more variance in this part of the space.
- It seems like the jacknife tests more or less confirm that there is not too much variation in the resulting fits, with maybe a ~0.5 sigma tension or so with M/L depending if we choose nu = 0.5 or nu = 1.5.
All together:
- I think we're really at a point to stop the modeling and decide what to report for our final results. I'm not too concerned about any of the M/L discrepencies since the minima are consistent with one another. Our biggest choice now is mostly what to do about nu=0.5 vs. nu=1.5 vs. what we actually want to quote.

Plots

M/L Fit Strangeness:
- First up, I've recreated the set of best-scaled 1d panels, this time coloring by the various parameters. My hope was to get a sense of why there seems to be this slight change in M/L as we approach K = 80 or so, which the further disappears as we continue to increase K.
  - Note that in these panels, I've marked the y-axis in increments of 5 to better see which points exactly are being added near K = 85 which might be swaying the M/L fit toward >2.6 rather than ~2.58 or so.
- My Current Theory (look at the "Color by BH" panel):
  - I'm still testing this a bit, but I think that the K=80 M/L bump/feature is a result of the rightmost blue points being "seen" when we increase beyond K = 80, and the GPR/dynesty "snapping" to the two low blue points near M/L~2.7.

Color by BH	Color by ML	Color by Rho0	Color by T	Color by Tmaj	Color by Tmin
[images/241108/color_by_BH.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241108/color_by_ML.png)	[images/241108/color_by_Rho0.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241108/color_by_T.png)	[images/241108/color_by_Tmaj.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241108/color_by_Tmin.png)

Robustness of Fits:
- I thought it'd be worthwhile to run a finer K grid to ensure that the weird behavior near K = 85 is real. To that end, I've run a set of GPR+dynesty runs startin from K = 40 to K = 120 for both nu = 0.5 and nu = 1.5.
- In the plots below, the different K's are plotted vertically, and every other point alternates between nu = 0.5 and nu = 1.5. You can see that, especially for non-M/L parameters, the results are incredibly robust.
- In general, the nu = 0.5 cases have uncertainties smaller than the nu = 1.5 case, and the nu = 1.5 case seems to full encompass all the nu = 0.5 posteriors.
- With all this said, I think it's just a matter of what we want to report here since no matter what, things are going to be essentially the same. I think it's more of what we want to show.
  - If I had to pick a single approach, I think we're fine to simply report one of the K>60, nu = 0.5 results since these are essentially totally identical to each other.

Plot
images/241108/K_NU_INVESTIGATION.png

Jacknife Testing:
- I've also run a set of jacknife tests for K = 60, 80, and 100 for both nu = 0.5 and nu = 1.5. Again as a quick reminder, the jacknife tests here throw out half the data under a given K value 10 times, and I'm plotting the resulting fits.
- In the upper half of the plots below, I've got the nu = 1.5 results, with the nu=0.5 results in the lower half.
- In addition to the 10 jacknife realizations for each K/nu, I've plotted the median value and median uncertainty range across the realizations in the shaded bands.
- Much as we see with the tests above, the median across the results is quite robust except in M/L where there is ~0.5 sigma tension or so.
- I think this more or less points to the fact that we can call the modeling here, and simply decide how we want to report our results.

Plot
images/241108/jacknives.png

A potential final cornerplot: I've taken the K = 100, nu = 1.5 result from last week (which had a very, very slight "island" at the 3 sigma level which I'm not sure we very much care about), and tried to create two publishable cornerplots for these data:
- Note that this rho0 converts to M15 ~1.1e12 Msun
- Remaining tasks on the Overleaf:
  - Update best-fitting model plots
  - Revise old numbers throughout text with their new values
  - Ensure that my description of the NNLS chi2 is sufficient. i think we're currently implying a kinematic chi2 throughout
  - Extract data from Boizelle+21 to ensure I'm plotting their MGEs correctly
  - Revise shapes to be volume-weighted rather than luminosity averaged. Kept them as luminosity averaged so far so we can comapre to the old results.
  - Remind myself of the CO-stellar comparison and their sources; ensure I am correcting for distance changes
  - Anything else?

Ts/UPQ	UPQ/Angles
[images/241108/nIter8_best_grid_D_and_E_grid_alpha_K100_nu1.5_Ts_241115-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241108/nIter8_best_grid_D_and_E_grid_alpha_K100_nu1.5_Shapes_Angles_241115-1.png)

Removing the Lowest Point

I quickly ran the same K/nu investigation and the jacknife test after removing the lowest most point which differed by ~15 in chi2 from the 2nd lowest.
- I hadn't examined this too closely, but despite there being a bit more scatter here, I thikn that these values are largely consistent with the results we obtained above.

K/nu Test	Jacknife Test
[images/241120/K_NU_INVESTIGATION_LOWER_REMOVED.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241120/jacknives_lower_dropped.png)