meeting 2025 04 08 n57 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki
Context
-
Below are the results from the 1000 models from yesterday, along with the "best scaled" results from the previous grid, bringing us to a total of ~3200 base models so far.
-
Takeaways:
- We're definitely moving in the right direction here! The chi2 for the new grid continues to drop and the appearance of the posteriors has improved as well. It's likely we need one more grid of models to round out the high side of the BH posterior and low side of the M/L posterior, but the rest of the parameters seem to be nicely constrained so far.
- To move forward, we have a few options depending on how confident we are in our ability to get the high BH/ML in the next set of models:
- Rather than submitting another 1000 models right away, it might be worth a smaller (say, ~250) models targetting this specific portion of the BH/ML space.
- Alternatively we could submit a few thousand dither 1 models to ensure that the BH and ML minima are fully resolved and then rerun a subset of those models using dither=3, or we could go straight to the dither 3 models.
- I think the dither1 approach to verify our coverage makes the most sense; it's quite cheap in terms of SU and we can always select a subset of the models rather than rerunning the full grid.
-
Just to keep track of things -- the latest best fitting model 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.
Diagnostics
- As a quick sanity check to see how much we've improved, here's a histogram of the previous "best scaled" chi2 values compared to the chi2 values from this latest grid where we only have the s=1.0 case. The median chi2 has improved by ~50:
| NNLS Chi2 Histograms |
|---|
| images/250408/nnls_chi2_comp.png |
- Now here's the 1d panels of the best scaled models from the previous grid with the s=1.0 models from the grid from last night. I've included two versions with different y-axis limits just to get a sense of how well the minimum is being resolved:
| Non-Zoomed | Zoomed |
|---|---|
| [images/250408/1d_panels.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250408/1d_panels_zoomed.png) |
- And I ran GPR + dynesty with the panels above for a few K and a few nu:
| K=60 | K=80 | K=100 | |
|---|---|---|---|
| nu=0.5 | [images/250408/grids12_best_scales_grid_3_base_grid_alpha_K60_nu0.5-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250408/grids12_best_scales_grid_3_base_grid_alpha_K80_nu0.5-1.png) | images/250408/grids12_best_scales_grid_3_base_grid_alpha_K100_nu0.5-1.png | |
| nu=1.5 | [images/250408/grids12_best_scales_grid_3_base_grid_alpha_K60_nu1.5-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/250408/grids12_best_scales_grid_3_base_grid_alpha_K80_nu1.5-1.png) | images/250408/grids12_best_scales_grid_3_base_grid_alpha_K100_nu1.5-1.png |
- I quickly built a proposed set of 1000 models using rejection sampling on the K=80, nu=1.5 case above:
| Proposed Set |
|---|
| images/250408/proposed_points.png |
- And as a real quick sanity check, here are the radial moments for the current best-fitting model:
| Radial Moments |
|---|
| images/250408/best_fit_moments.png |
