meeting 2026 03 06 gw - JacobPilawa/TriaxSchwarzschild_wiki_6 GitHub Wiki

Context

Following up on some of the results from last time on the relationship between the mass difference the Cluver14 mass, the GSMF construction, and some attempts at trying to get Steve Taylor's website working.

I've double checked the plots from last time, showing the mass difference (LM24 - Cluver14_clipped) as a function of (Cluver14_Clipped) masses. The trend that we saw in the last meeting does appear to hold (though in the last meeting I did have a bug in my linear fits to the data; the lines from last time were being fit to the binned means (some of which were extreme outliers due to only containing a few galaxies) causing them to be far offset from the main cloud of points).
- First, here are a few diagnostic plots I've used to check what we've been looking at:

Case	Delta M vs. M	Delta M vs. z, binned by M	Delta M vs. M, binned by z
Cluver	[images/260306/Cluver14_clipped_by_z.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/Cluver14_clipped_by_mass.png)	images/260306/Cluver14_clipped_panel.png
LM24	[images/260306/LM24_cluver14_clipped_by_z.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/LM24_cluver14_clipped_by_mass.png)	images/260306/LM24_cluver14_clipped_panel.png

And highlight the Cluver specific results a bit more clearly (in a stlye we've looked at before):

Mass Resdiduals, Single	Mass Residuals, Panels
[images/260306/mass_residuals_single.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/mass_residuals_zbins.png)

I've then fit two different GPs to the data above, one of them being 1D in Cluver14 mass and the other being 2D in Cluver14 mass and redshift. Taking the single panel results displayed just above, I fit 10 GPs to the data (sampling 3000 points each time), and get the following (the right-most panel is the residuals after "correcting" the masses with the 1D GP)

GP Fit	GP fit with Contours	"Corrected" Mass Residuals	Histograms of the Residuals
[images/260306/gp_fit_scatter.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/gp_kde_contours.png)	[images/260306/gp_corrected_kde.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/histograms_by_zbin.png)

From the corrected panel, it seemed to me like there is additional redshift dependence not being accounted for, so I added z to the GP fit. Here's one way of visualizing this:

Mean Difference in 2D	Mean GP Surface	Corrected Surface
[images/260306/mean_diff_heatmap_before_correction.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/2d_gp_surface_mean_and_uncertainty.png)	images/260306/mean_diff_heatmap_after_correction.png

And one other way to visualize the 2D GP is to look at the 1d Delta M vs. M panel with the 2D correction vs. the 1D correction:

1d vs. 2D GPR Correction
images/260306/1d_vs_2d_correction_comparison.png

I'm still having a hard time getting anything reasonable from the poisson process approach, and I think I need just some help troubleshooting things. Here are some of the things I've tried, but it really feels like trying to find a black cat in a dark room a bit.

Just to get things running, I have a "fiducial" case I'm basing everything off of. This case make sthe following choices:
- Sampling 1000 random galaxies from my catalog.
- Adjusting "volumefactor" in the code to be ~0.7
- Including Leja as a chi-square constraint in the likelihood
- Prior ranges are the same as in Emily's paper
- Integral area is over a 2D box defined by zmin, zmax, Mmin, Mmin
The results from this are shown below, but the takeaway is that the posteriors are all running into the boundary, and the resulting GSMF is totally inconsistent with anything reasonable:

Posteriors	GSMF Samples
[images/260306/260305_fiducial_posterior.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/260305_fiducial_gsmf.png)

If I remove the Leja constraint from the likelihood, I get essentially the same thing, but apparently the "alpha1" parameter converges to ~0.5:

Posteriors	GSMF Samples
[images/260306/260305_fiducial_no_leja_posterior.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/260305_fiducial_no_leja_gsmf.png)

I've also tried to experiment with the integration bounds in the calculation for N_lam by interpolating a boundary in the (M,z) space defined by where we have galaxies:
- In the absense of anything better, I'm getting these bounds by linearly interpolating the data after binning it. The bounds are the 2nd to the 98th percentile of the binned distribtuions.

New Integration Bound Test
images/260306/test_integration_domain.png

The result from this test is essentially identical to the case where I remove the Leja constraint, but the alpha1 parameter changes slightly to near 0.
- Another side effect is that dynesty takes quite long since the double integral over the interpolated bounds is much more computationally expensive. It took maybe 2 hours to run.

Posteriors	GSMF Samples
[images/260306/test_posterior_fast_grid_CLAUDE.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/test_gsmf.png)

Here's the "fiducial" case but using 10k galaxies instead of 1000 from my catalog. Really just trying to get a sense of the dependence on the input catalog:

Posteriors	GSMF Samples
[images/260306/260306_10k_test_posterior.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/260306_10k_test_gsmf.png)

Here's a case where I run the "fiducial" test with 1000 galaxies, but boost all the masses by 1 dex. Just trying to see how the masses manifest, and if in fact correcting the masses to be consitent with LM24 will move anything around.

Posteriors	GSMF Samples
[images/260306/260306_1k_mass_boosted_1_dex_posterior.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/260306_1k_mass_boosted_1_dex_gsmf.png)

I've also tried boosting by 1dex and relaxing the Leja constraint in the likelihood:

Posteriors	GSMF Samples
[images/260306/260306_1k_mass_boosted_1_dex_no_leja_posterior.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/260306_1k_mass_boosted_1_dex_no_leja_gsmf.png)

Perhaps most interesting, I've played around iteratively with the prior ranges and can start to get several of the parameters to converge, albeit to pretty non-sense values:
- I've been trying to improve this further by playing with the prior for the uncoverged parameters, but dynesty's sampling has gotten extremely slow. Trying to improve this currently.

Posteriors	GSMF Samples
[images/260306/260306_playing_with_prior_posterior.png]]](/JacobPilawa/TriaxSchwarzschild_wiki_6/wiki/[[images/260306/260306_playing_with_prior_gsmf.png)