meeting 2023 08 17 n57 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

This bullet contains diagnostics for the tests I've been running on the N57 MGE and the GPR + dynesty routine to try to mitigate the bimodality in our posteriors.

There are more complete summaries under each bullet below, but in very brief:

• Regularized and unreguralized MGEs are essentially identical, though the unregularized MGE often has 2 or 3 more MGE components and has quite small q in the outer regions.
• The bi-modal feature seems to persist in our posteriors no matter the best-scaled selection/thinning/jacknifing.
  • One nice thing is that the 2 sigma and 3 sigma regions are remarkably consistent no matter what I seem to do. The 1 sigma contours might shift a bit depending on the exact choices.

In short: I think I could increase the smoothing in the 2d posterior panels from a purely plotting perspective if we really wanted to ``fill in'' the ridge, but at this point, I think it might be best to simply report the bimodal features and note that the actual 1d chi2 panels are very broad and that we should only really interpret the 2 sigma and 3 sigma contours. I sort of believe that Tmaj might not have that strong of a constraint in this case, and I worry that the thinning + jacknifing procedure is stepping too far away from the data itself.

• I'm still playing around with the jacknife acceptance fractions and will continue to try to reproduce the smoothed contours we have seen before with rather extreme jacknifing.

• When using the best versions of the scaled models, changing the cutoff K to higher and higher values does not seem to appreciably change the results. There is a bit of a difference in the 3 sigma contours when using K<50 or so, but this could likely be remedied by increasing nSamples. I instead just use K = 50 for the cutoffs below (this corresponds to roughly 6 sigma in 6D).
• When taking the set of best scaled models (roughly 6500 models) and running the thinning routine gives ~1000 models out to 6 sigma. GPR + dynesty on the thinned version of the best-scaled models shifts the best fit values slightly (~1/4 sigma or so), but does not really impact the 2 and 3 sigma contours. Given this, it seems to make the most sense to not run the thinning routine. For some of the testing below, though, I stuck with the thinned versions of the models becasue they run much, much faster through GPR + dynesty.
• At first glance, jacknifing the points only within 1 sigma appears to step in the right direction, but I am still playing around with that a bit and finding the right balance of jacknife fractions. I think this is realistically the best way to smooth out the bimodal features, but I also don't know if that's really what we want to be doing at this stage.
  • Doing the same test but keeping/jacknifing all points within 2 sigma gives essentially the same results and contours.