meeting 2024 10 31 n315 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

  • Happy Halloween!

    • I've gone through and processed our suggestions from yesterday, mostly regarding Grid D and rejection sampling points. I've run dynesty + GPR on the grid D points alone (restricted to the low Tmin section of the space), and built some rejection sampled proposals from the Grid D models alone.
    • The Grid D only GPR + dynesty runs are surprisingly really nice looking! The resulting posteriors and favored parameters are quite consistent across different Ks/nuts, and also quite consistent from the results with all the cubes. The upside is that these all run much faster since we're restricting the Tmin range to Tmin<0.3.
    • The rejection sampled proposed points are all mostly looking reasonable and consistent with one another too. I've got some additional information and diagnostics below.

  • Moving forward:

    • I think it'd be reasonable to move forward with K = 100, nu = 1.5 set of proposed points, though the K = 60/80/100 nu=0.5/1.5 set of points are all virtually identical so I don't think we'd get appreciably different answers. I only chose K = 100, nu = 1.5 since we're including lots of models still and sticking with the usual nu of 1.5.

Grid D Alone

  • First, here are some cornerplots considering the Grid D points with Tmin<0.3 alone.
    • Again, I think you can safely ignore the results with K = 40. At this cutoff level, we have ~50 models included in the fit. Here's a plot of the number of models vs. Chi2 for the Grid D models with Tmin < 0.3:
Grid D, Tmin < 0.3 Only
images/241031/CDF.png
  • And here are the resulting cornerplots from Grid D Tmin<0.3:
K=40 K=60 K=80 K=100
nu=0.5 [images/241031/low_trim_trimmed_grid_D_grid_alpha_K40_nu0.5_Ts_241031-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241031/low_trim_trimmed_grid_D_grid_alpha_K60_nu0.5_Ts_241031-1.png) [images/241031/low_trim_trimmed_grid_D_grid_alpha_K80_nu0.5_Ts_241031-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241031/low_trim_trimmed_grid_D_grid_alpha_K100_nu0.5_Ts_241031-1.png)
nu=1.5 [images/241031/low_trim_trimmed_grid_D_grid_alpha_K40_nu1.5_Ts_241031-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241031/low_trim_trimmed_grid_D_grid_alpha_K60_nu1.5_Ts_241031-1.png) [images/241031/low_trim_trimmed_grid_D_grid_alpha_K80_nu1.5_Ts_241031-1.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241031/low_trim_trimmed_grid_D_grid_alpha_K100_nu1.5_Ts_241031-1.png)

Rejection Sampling Information and Diagnostics

  • I've run our rejection sampling scheme for some different Ks and different nus, again limiting myself only to Grid D.

    • As a quick reminder, the rejection sampling scheme runs 10 GPR + dynesty iterations, throwing out half the data each time. We then sample from the union of the 10 different sets of posteriors.
    • I've fit the Gaussian process for a variety of different Ks and nus (specified below), and I am using a cutoff of 20.06 for accepting or rejecting the proposed point (which corresponds to 3sigma in 6D).
    • The low K (40 or 60) fits seem to be too broad for our use, likely because outside the K cutoff, the Gaussian process is "flattening" to some reasonable value that ends up allowing many of the proposed points. Nu = 0.5 are a bit more "flexible" of fits and seem to "round out" the posteriors a bit better, but I think a bit artificially.

  • Moving forward:

    • With the above in mind, I think we're fine to use any of the K = 80 or K = 100 posteriors for the rejection sampling, and the net result of proposed points are not that different from one another.
    • Note that I am currently allowing the proposed points to be down to 0.001 for Tmin and Tmaj, which allows us to probe closer to the boundaries/beyond the original Grid D boundaries.

  • And here are the actual plots:

    • The K/nu listed below are the settings I'm fitting the gaussian process with.
    • The black points are 1000 model points drawn using rejection sampling, and the contours plotted show a random jacknife iteration set of contours so you can see what GPR/dynesty wants for the best fit compared to the new model proposed locations.
    • One note: some of the posteriors have hard edges, but this is an artifact of our old model boundaries which had hard cutoffs at Tmin = Tmaj = 0.01. The new proposed models go down to Tmin = Tmaj = 0.001, which results in some model points being proposed on the "opposite side" of the posteriors.
K=40 K=60 K=80 K=100
nu=0.5 [images/241031/points_grid_alpha_K40_nu0.5.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241031/points_grid_alpha_K60_nu0.5.png) [images/241031/points_grid_alpha_K80_nu0.5.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241031/points_grid_alpha_K100_nu0.5.png)
nu=1.5 [images/241031/points_grid_alpha_K40_nu1.5.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241031/points_grid_alpha_K60_nu1.5.png) [images/241031/points_grid_alpha_K80_nu1.5.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241031/points_grid_alpha_K100_nu1.5.png)
  • Here's perhaps a better set of plots which directly compares the distributions to each other and to the Grid D models:
nu = 0.5 nu=1.5
[images/241031/proposed_comp_nu0.5.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_5/wiki/[[images/241031/proposed_comp_nu1.5.png)