meeting 2024 10 25 n315 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

  • Here's an update following our meeting from this week!

    • I've added the additional scalings for Grids C and D (specifically added s=0.985, 0.998, 1.002, and 1.015 to the existing s=[0.99,0.995,1.0,1.005,1.01] scalings. We did this because it seemed like some of the best-performing models still hadn't "bottomed out" on their scallop shapes.
    • I've also reprocesses our final posteriors with the addition of these new scalings, and the parameters seem robust to these additional scalings/models.

  • Still working on a few things...

    • I've run the remaining ~100 models from Grid Bprime and am processing those results now. I'll upload the full set of 300 d1 vs. d3 hopefully this afternoon, working on it now.
    • I also am fiddling around with a proposed set of grid points based on rejection sampling off the posteriors below. Running the jacknife iterations now which will then be used for accepting or rejecting the points.

Plots

  • First, here are some summary plots for each of the cubes.
Grid A Grid B Grid B Prime Grid C Grid D All Base Models All Best Scales
[images/241025/241024_Grid_A_Ts.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/241024_Grid_B_Ts.png) [images/241025/241024_Grid_Bprime_Ts_b.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/241024_Grid_C_Ts.png) [images/241025/241024_Grid_D_Ts_b.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/241024_Ts_Base.png) images/241025/241024_Ts_best_b.png
  • And here's a quick histogram of the NNLS chi2 for each of the grids, showing that we are in fact rapidly reaching the low chi2 area with our rejection sampled models.
Plot
images/241025/hist.png
  • And here are some updated posteriors with the new scalings added to the "best-scaled" versions.
    • Note that I've fixed the axis issue so that now the posteriors are all plotted on the same scale. I'll make the scales a bit prettier when we settle on a final K/nu, but this should work for now for us to compare all the results:
    • The top and bottom set of posteriors are identical, but the top set reports T's and upq, whereas the bottom set reports upq and angles:
K=60 K=80 K=100
nu=0.5 [images/241025/trimmed_all_grid_alpha_K60_nu0.5_Ts_241025-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/trimmed_all_grid_alpha_K80_nu0.5_Ts_241025-1.png) images/241025/trimmed_all_grid_alpha_K100_nu0.5_Ts_241025-1.png
nu=1.5 [images/241025/trimmed_all_grid_alpha_K60_nu1.5_Ts_241025-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/trimmed_all_grid_alpha_K80_nu1.5_Ts_241025-1.png) images/241025/trimmed_all_grid_alpha_K100_nu1.5_Ts_241025-1.png
K=60 K=80 K=100
nu=0.5 [images/241025/trimmed_all_grid_alpha_K60_nu0.5_Shapes_Angles_241025-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/trimmed_all_grid_alpha_K80_nu0.5_Shapes_Angles_241025-1.png) images/241025/trimmed_all_grid_alpha_K100_nu0.5_Shapes_Angles_241025-1.png
nu=1.5 [images/241025/trimmed_all_grid_alpha_K60_nu1.5_Shapes_Angles_241025-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/trimmed_all_grid_alpha_K80_nu1.5_Shapes_Angles_241025-1.png) images/241025/trimmed_all_grid_alpha_K100_nu1.5_Shapes_Angles_241025-1.png

Grid B Prime Completed

  • I've filled out the remaining ~100 models from Grid Bprime. There's actually hardly a change in any of the results, but here are two plots showing a quick comparison of the d1 and d3 grids:
1-to-1 CDF
[images/241025/nnls_1_to_1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/CDF.png)

Investigating Scalings for Grids C and D

  • One question from over the weekend -- how much do the new scalings improve our coverage? Specifically, can we identify which models have "bottomed out" or not?

    • To investigate this a bit, I've gone ahead and fit quadratics to all of the (scale) vs. (NNLS chi2) data for Grids C and D. Note that I'm currently checking for a minimum by looking at the numerical derivatives -- if they sign of the numerical derivative changes, we mark it as "bottom out"
    • As you can infer from the plots above, and more obviously from the plots below, Grid C seems to be on the less-massive side, and Grid D seems to be on the more-massive side.
    • This suggests to me that we can add a few more scalings to the high end of Grid C and low end of Grid D.

  • I've also plotted the "bottomed out" vs. "non-bottomed out" models in a cornerplot style plot, but it's not obvious to me that this is very telling apart from where we can expand our scalings.

  • First, here are the 1d chi2 vs. scalings for Grids C and Grid D, split by those which bottom out vs. those that don't:

    • For reference, about ~2/3 of the Grid C models have not bottomed out yet, and about ~1/2 of the Grid D models are still non-bottomed out. I think we can likely increase this fraction, but unsure how many new models we will add to the minimum region since we can't change the shapes with the scalings, so we're likely selecting models which have decent mass parameters AND shapes.
Grid C Grid D
Bottomed Out [images/241025/Grid_C_bottom_out.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/Grid_D_bottom_out.png)
No Bottom Out [images/241025/Grid_C_no_bottom_out.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/Grid_D_no_bottom_out.png)
  • And now here are the 2d plots I described above, marked accoringly. Note that the parameter order here is (BH, ML, Rho0, T, Tmaj, Tmin), but are labelled simply as "param_i" currently.
Grid C Grid D
[images/241025/Grid_C_pair_plot_2.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241025/Grid_D_pair_plot_2.png)