meeting 2024 02 06 n315 - JacobPilawa/TriaxSchwarzschild_wiki

Context

I've finished running our second d3 grid and added a number of scalings. Initially, we tried to run the convex hull sampling routine but the geometry of the hull near high Tmin was a bit strange, so we opted for a simple zoom in on the d1 models we ran last week.
The d1 models were over the following range:
- BH = [5e8, 4e9]
- ML = [2.0, 3.2]
- rho = [1.7e9 6.5e9]
- T = [0.5,0.99]
- Tmaj = [0.01,0.5]
- Tmin = [0.4,0.99]
We then selected the models which were within 1000 of the d1 minimum, leaving us with 729 new models to run with d3. In the results below, I've also added 6 scalings to this grid, at 1, 3, and 5 percent above and below the base set of models.
Takeaways: Things are looking really nice! There aren't huge changes in the overall landscape. We instead just are continuing to decrease our kinematic chi2 and seem to be carving out a minimum in all of our parameters. The Mitchell h6 data seem to still be struggling to be fit well. With all the models I have now, I am going to start looking into whether or not one moment in particular is driving the minimum in a particular direction. I'm also going to re-run our convex hull routine to see if that situation has improved.

First, here's the comparison between the d1 and d3 chi2s for this grid. Again, we have an excellent correlation between the two grids which suggests that the d1 models are really helping us decide what will be "good" models.

d1 vs. d3 chi2

Here are the 1d chi2 vs. parameters for the 729 base models, all 729*7=5103 scalings, and the results of selecting the best scaled version from these.

729 Base Models	All Scalings (729*7)	Best Scalings(729 Models)

Our total set of base models is now 866+729 = 1595. If we include scalings, we have a total of 11866 + 7297 = 14,629 models! Pretty impressive.
First, here's a quick comparison of the "CDF" of our models. I'm comparing the 1595 base models to the 1595 "best scaled" versions of the models and the set of all scaled models here. Note that the scaling + selecting of the best models really does improve our coverage of the minimum.
- Note the plot on the right and left are the same, just with different y-axis limits:

Cutoff K	Num. Models < min(chi2) + K [Base]	[Best Scales]	[All Scales]
10	1	1	5
50	3	7	23
100	9	26	75
250	77	206	722
500	440	816	3699
750	875	1268	7120
1000	1207	1475	9811
1500	1530	1586	12801
2000	1595	1595	13922
2500	1595	1595	14300

Plot

Here are 1d panels of chi2 vs. parameters, showing the combination of the two dither 3 grids we have so far (I'm calling them Grid A and Grid B). Included in here are plots with all the scalings, only the base set of models, and the "best-scaled" versions of the two grids.

729+866 Base Models	Best Scalings (866+729)	All Scalings (14,629 models)

Now that we have ~1600 "good" models between the two grids, with ~a few hundred model points within ~a few hundred of the minimum, I think we can start looking at the dynesty posteriors a bit more seriously. Here are some dynesty runs with varying parameters.
Note that I am specifically only using the "best-scaled" verison of models in these posteriors.