meeting 2024 11 04 n315 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

  • Here are some diagnostics relating to Grid E, the points generated from rejection sampling based on Grid D (Tmin < 0.3).

  • Takeaways:

    • The results are looking substantially improved compared to our results which ended with Grid D alone. Grid E's points seem to lead to a clear minimum in Tmaj and Tmin which had a ~tentative minimum previously.
    • One interesting note is that the high T landscape seems to shift a bit, but it's a bit hard to tell with the non-scaled models here. I think that this "wedge" at high T might improve with scalings added, but it's also not obviously contradicting what we had seen before. And our posteriors seem to do fine with this wedge still.

  • New takeaways post scaling:

    • Seems like things are converging well, with a few random small things (M/L for low K seems to be near the upper boundary, and there is a slight, slight bimodal feature which seems to appear in the shape space). These issues largely are mitigated using very high K, essentially including all models from Grid D and E.

Base Models

  • First up, here are the 1d panels for the base set of models for Grids D and E plotted in the relevant spaces:
T Space Angle Space UPQ Space
  • And here's the result of running GPR/dynesty on the base models between these two grids. I've included versions with both nSamples = 1 and nSamples = 8, and there is virtually no difference.
nSamples = 1 Results
nu K=60 K=80 K=100
0.5
1.5
nSamples = 8 Results
nu K=60 K=80 K=100
0.5
1.5

Grids D and E Scalings

  • Here's a quick comparison of the Grid D and Grid E sets of all scaled models. The right and left are Grids D and E respectively:
Plot

Best Models

  • And now some of the diagnostics for the set of best scaled models. First up, here's the 1d panels:
T Space Angle Space UPQ Space
  • And here's a CDF-style plot of the NNLS chi2 values:
CDF
  • And here's the result of running GPR/dynesty on the best models between these two grids. I've included versions with both nSamples = 1 and nSamples = 8, and there is virtually no difference.
nSamples = 1 Results (Ts and UPQ)
nu K=60 K=80 K=100 K=500 (All Models)
0.5
1.5
nSamples = 8 Results (Ts and UPQ)
nu K=60 K=80 K=100 K=500 (All Models)
0.5
1.5
nSamples = 1 Results (UPQ and Angles)
nu K=60 K=80 K=100 K=500 (All Models)
0.5
1.5
nSamples = 8 Results (UPQ and Angles)
nu K=60 K=80 K=100 K=500 (All Models)
0.5
1.5
  • And here's a more direct comparison of the nSamples = 1 vs. nSamples = 8 results. This is a veritcal plot showing the 1 sigma results for each of the cornerplots above. In black are the nSamples = 1 results, and the nSamples = 8 results in red. The two sets of results are essentially identical at the 1 sigma level.
Vertical

Removing the Low Point Between 0.9<T<0.95

  • The strange bimodal feature in T stood out to me, so I tried ot remove the single low-lying point near 0.92 or so, and here are the cornerplots from running those tests. Note that these all use nSamples = 1 which should not be different (that much) from the nSamples = 8 case.
LOW REMOVED: nSamples = 1 Results (Ts -- didn't get a chance to make the final cornerplots for this but things look less bad? Only made at the last minute, need to check this a bit closer)
nu K=60 K=80 K=100 K=200 K=500 (All Models)
0.5
1.5

Jacknife Tests

  • I wanted to investigate the very very slight bimodal features which seem to be present in the landscapes/just generally wanted to test the stability of the GRP and dynesty fits. I've run jacknife tests on our best scales Grid D/E, throwing out half the data and running 10 GPR + dynesty iterations. Here are some results.
    • There's quite a bit of bouncing around here, but I think the general trend is that including all the points makes the resulting fits much more stable (using K=200 or above).
Again, take these with a bit of a grain of salt -- I need to look into some of the "weird" results a bit more closely still. Just haven't gotten around to that yet.
K=60 K=100 K=200 K=500
nu=0.5
nu=1.5
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