meeting 2023 10 13 - JacobPilawa/TriaxSchwarzschild_wiki_5 GitHub Wiki

Context

  • I've computed the Delta Chi2 cutoffs we need to impose in order to recover approximately the same width for the uncertainties between the two methods, as we've discussed the meeting yesterday.

    • In practice, I've essentially done what I described yesterday, where I gradually decrease the "cutoff" I impose until the difference in the uncertainty widths changes sign, signifying that the sqrt(2Nkin) uncertainties had become smaller than the likelihood uncertainties.

  • The result is more or less what we were guessing yesterday -- **we need to impose a cutoff of something like ~2.63 in chi2 (with standard deviation of 1.05) in order to obtain essentially the same uncertainties for the black hole mass as provided by the sqrt(2Nkin) method). This is in line with what Emily found from the coverage probability approach, too (if I remember, she needed something like a cutoff of Delta Chi2 = 3.1).

Here are the 1d panels which result from applying these cuts -- the model points are in black, the cutoff we need to impose is the horizontal blue line, the best-fit black hole mass from our likelihood approach is in purple, and the resulting uncertainties from the cutoff approach is plotted in red.
Plot
And here's a histogram of the 25 different cutoff values we need to impose -- the resulting distribution is not Gaussian, but I plotted a Gaussian with the mean and standard deviation of the data on top for reference. It's certainly true that we need something much larger than Delta Chi2 = 1
Plot
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