meeting 2024 02 14 n315 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

  • I've run a third grid of dither 3 models, this time using our rejection sampling routine (see previous bullet for the comparison between convex hull and rejection). This includes minimization with a few different scalings as we normally do.

  • Takeaways:

    • One thing that stood out to me immediately is that these rejection sampled models perform much, much better in chi2 than the previous two grids. Additionally, the chi2 variation for these models is much smaller (on the order of a few hundred) compared to the typical variation of a few thousand for the previous two grids. In this sense, the rejection sampling routine seem to work exactly as we had hoped.
    • Things are still looking nice, but we might be coming up on a slight issue -- a small number of models were accepted from the rejection sampling routine at Tmin near 0, and these in fact are performing really quite well, moreso than the previous minimum at high Tmin. This in turn has caused GPR + dynesty to be a bit strange, but it's not obvious to me that anything is actually incorrect with these models. I just don't know how to reconcile the previous high Tmin minimum we were seeing with the new low Tmin, good-fitting models.

Diagnostics

1d Panels

  • First, here's a variety of 1d panels showing the chi2 vs. parameters for this grid/all grids/selecting best scalings:
Grid C Base Models Grid C All Scales Grid C Best Scales All Base Models All Scaled Models All Best Scales
Non Zoomed
Zoomed
I've also included plots in the shape and angle space for all scalings here for completeness.
Angle Space Shape Space Shape Space (ZOOMED)

GPR + Dynesty

I think in large part due to the strange sampling in the space we currently have, dynesty has been getting stuck in many of the cases I am trying. I wanted a few examples for the meeting so here is what I was able to get fully run. Specifically, these using K = 150, 200 (for about 800 and 900 models each), for nu = 1.5. I also was curious what happens if we simply ignore the low Tmin models, (about 40 in total), so I have examples where these models are removed from the fit as well.
All Tmin Tmin > 0.4
K=150
K=200

Chi2 Per Moment

  • Motivated mostly be the strange low-chi2 region at low Tmin, I was curious how the chi2 per moment looks for all the models we have so far:
v sigma h3 h4 h5 h6 h7 h8 h9 h10 h11 h12
Total Chi2
Fractional Chi2

Best Fit Model Diagnostics

  • The current best fit model has (BH, ML, Rho0, T, Tmaj, Tmin) = (2.865e9, 2.47, 3.13e9, 0.90, 0.0543, 0.0238), and here are some of the diagnostics for this model:
Label Plot
Kinematics
Beta
Large heatmap of the chi2 per bin/moment
Plot
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