meeting 2023 10 12 - JacobPilawa/TriaxSchwarzschild_wiki

Context

Here are just some plots in case we need them for discussion for the meeting -- these are all the cornerplots from the dynesty runs, as well as the individual chi2 vs parameters

Cutoffs for Chi2 <1 Case

Diagnostic information on creating the confidence intervals for the delta chi2 < 1 cases

* We saw that some of the Chi2<1 regions of the 1d panels are quite sparse, and imposing this cut leaves some models with only 1, 2, or 3 models in this interval * I went ahead and did the following: * first, impose the chi2 of 1 cut and get intervals for which there are data * if the resulting uncertainty is one-sided, use the one-sided error on both sides * if there are no other models, gradually increase the cutoff until a second model lands in the interval, at which point treat it as a second interval

The resulting values are:
- G1 r1: $1.48^{+0.88}_{-0.37}$
- G1 r2: $1.14^{+0.59}_{-0.59}$ --> symmetric interval imposed
- G1 r3: $1.89^{+0.07}_{-0.84}$
- G1 r4: $2.29^{+0.70}_{-0.70}$ --> symmetric interval imposed
- G1 r5: $1.33^{+0.52}_{-0.52}$ --> symmetric interval imposed
- G2 r1: $2.03^{+0.10}_{-0.66}$
- G2 r2: $1.38^{+0.62}_{-0.16}$
- G2 r3: $1.12^{+0.52}_{-0.12}$
- G2 r4: $1.42^{+0.48}_{+0.48}$ --> P2r4: 2.1 cutoff and then symmetric error
- G2 r5: $1.13^{+0.08}_{-0.08}$ --> symmetric interval imposed
- G3 r1: $1.42^{+0.41}_{-0.41}$ --> symmetric interval imposed
- G3 r2: $0.40^{+1.03}_{-1.03}$ --> symmetric interval imposed
- G3 r3: $1.01^{+0.04}_{-0.04}$ --> P3r3: 1.6 cutoff and then symmetric error
- G3 r4: $1.37^{+0.25}_{-0.25}$ --> symmetric interval imposed
- G3 r5: $1.35^{+0.34}_{-0.34}$ --> symmetric interval imposed
- G4 r1: $1.84^{+0.90}_{-0.47}$
- G4 r2: $1.81^{+0.23}_{-0.23}$ --> symmetric interval imposed
- G4 r3: $2.20^{+0.21}_{-0.82}$
- G4 r4: $1.32^{+1.13}_{-1.13}$ --> symmetric interval imposed
- G4 r5: $1.79^{+0.73}_{-0.73}$ --> P4r5: 1.2 cutoff and then symmetric error
- G5 r1: $1.14^{+0.59}_{-0.02}$
- G5 r2: $1.47^{+0.78}_{-0.10}$
- G5 r3: $2.04^{+0.88}_{-0.88}$ --> symmetric interval imposed
- G5 r4: $1.48^{+0.40}_{-0.38}$
- G5 r5: $1.22^{+0.65}_{-0.65}$ --> symmetric interval imposed