meeting 2025 04 09 n57 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

  • I've added an additional 1000 rejection sampled models to the N57 grids based on the best-scaled + third grid (s=1.0) set of models! This brings out total set of model her to ~4200:

    • 2200 of these were from our old grids which we had rerun and run scalings for (6 scalings + 1 set of base models)
    • 1000 models are from rejection sampling on the contours of the 2200 best scales
    • The final 1000 models are built from rejection sampling off the ~3200 models above.
    • The current best fitting NNLS chi2 model is actually from the third grid, and has an NNLS chi2 of 1654.59, and we have (215)(8)+(41)(6) = 1966 constraints, giving a reduced chi2 of 0.84 so far.

  • Takeaways:

    • Looks like we found the minimum here! The newest models seem to resolve the full 3 sigma contours on BH and M/L now. The only parameter left "unconstrained" is Tmin which effectively wants to be near 0.
    • The new models don't seem to significantly drop in the chi2 value, further sign that where we're at right now is likely the final minimum. If we wanted to double check this, we could run say a +/- 1% scaling on these latest models/the previous s=1.0 grid, but it's not clear we actaully need to do that right now (also mentioned below)

  • Moving forward:

    • I personally think we're good to move forward with the writing/we're likely finished with the models! I'm creating production level plots of our current results and will place them on this page when they're ready. I'll ensure that we're correcting our masses to the angular diameter distance rather than the SBF distance we're currently using.
    • If we really wanted to run anything else, I thikn we would benefit most (but not much improvement) from scalings based on the most recent 1000 models. This set of models seems to straddle both sides of the masses and would thus benefit from positive and negative scaling. With that said, our posteriors already look quite nice and are consistent across cases, so I'm not sure it's entirely necessary.

Diagnostics

  • First, here are the 1d panels for the best scaled + third grid (s=1.0) models + fourth grid (s=1.0) models:
1d panels 1d panels Zoomed
[images/250409/1d_panels.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250409/1d_panels_zoomed.png)
  • And I ran these 1d panels through out GPR and dynesty routines:
    • The different K and nu are remarkably consistent with one another, with each case agreeing with all other cases virtually identically.
K=60 K=80 K=100
nu=0.5 [images/250409/grids12_best_scales_grids_34_base_grid_alpha_K60_nu0.5-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250409/grids12_best_scales_grids_34_base_grid_alpha_K80_nu0.5-1.png) images/250409/grids12_best_scales_grids_34_base_grid_alpha_K100_nu0.5-1.png
nu=1.5 [images/250409/grids12_best_scales_grids_34_base_grid_alpha_K60_nu1.5-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250409/grids12_best_scales_grids_34_base_grid_alpha_K80_nu1.5-1.png) images/250409/grids12_best_scales_grids_34_base_grid_alpha_K100_nu1.5-1.png
  • Just as a quick sanity check, here's a cumulative distribution of the chi2 values to get a sense of how many models are included in each K.
Cumulative Chi2 Distribution
images/250409/cumulative_dist.png

Email Follow Ups:

  • Here's a quick histogram showing the improvement of each grid, with the two rejection grids separated out:
NNLS Chi2 Histograms
images/250409/chi2_histograms.png
  • I also have the number of models as a function of K for a few key values of K. Also note that the full distribution is just above on this page:
K Number of Models <K
20 266
30 1099
40 1752
60 2393
80 3127
100 3700
  • I also ran GPR + dynesty on ONLY the red points in the panels above. Note that the Fourth Grid had only ~1000 models, all of which fall within 60 of the minimum so I ran GPR + dynesty only using K=40 (~900 models) and K=60 (~1000 models).
    • The results using only the red points are essentially identical to the full set of points within our rounding.
K=40 K=60
nu=0.5 [images/250409/grid4_base_only_grid_alpha_K40_nu0.5-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250409/grid4_base_only_grid_alpha_K60_nu0.5-1.png)
nu=1.5 [images/250409/grid4_base_only_grid_alpha_K40_nu1.5-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250409/grid4_base_only_grid_alpha_K60_nu1.5-1.png)