meeting 2024 01 27 n315 - JacobPilawa/TriaxSchwarzschild_wiki

Context

I've run the first dither 3 model grid by taking the 866 best performing models (all of which were within 1500 of the minimum from the first two dither 1 grids).
The results broadly look nice!
- Roughly speaking, there is simply an offset of ~300 between the d1 and d3 models, with the d3 models having the larger chi2.
- Of the 866 models we submitted, 821 of them remained within 1500 of the minimum despite the general offset.
- The line of best fit between the two sets of points has a slope of 1.08 and an intercept of ~290.
One thing to note that I am still trying to figure out:
- I've plotted the chi2 associated with each moment as a function of parameters and computed the fractional contribution to the total chi2;
- It seems like the h6 data that we're currently using is contributing something like ~25% of the total chi2 of our models. The other moments are contributing at most ~12.5% or so to the total which is what I would expect if things were distributed evenly.
- Additioanlly, some of the individual landscapes are quite lobsided/certain moments seem to favor distinct portions of the space.
- I'm not sure if at the current stage this is a concern, but it's something that stood out to me as being extra-ordinary.

Plots

First, here's the 866 model point chi2's plotted against each other:

Plot

And the breakdown of chi2 as a function of cutoff K for these new d3 models:

Cutoff K	Num. Models < min(chi2) + K
10	1
50	1
100	4
250	36
500	178
750	371
1000	545
1500	821
2000	866
5000	866

Here's a side by side comparison of the 1d landscapes for the two sets of models

Plot

I've run a quick set of dynesty plots, knowing full well that the models are currently greatly undersampled/are to be taken with a massive grain of salt.

Cutoff K	nu=0.5	nu=1.5
250
500
1000

I've pulled out two specific dynesty runs for comparison -- these are the K=1000 cut off, nu = 1.5 results for the d1 and d3 grids side-by-side. They agree very, very well which is encouraging! Again, I know that at this stage, the dynesty resulst are hard-to-interpret at best, but it's nice that the results are not all over the place.

d1 results	d3 results

Broken down by moments:

I was curious how the individual moment landscapes were looking for the 866 dither 3 models we just ran, so I've plotted the 1d panels broken down by moment:
Another useful thing to look at is the chi2 associated with each moment for the best fitting model:

Moment	chi2	fraction
all moms	3521.26	1.000
V	220.879	0.063
sigma	348.142	0.099
h3	335.068	0.095
h4	436.911	0.124
h5	445.013	0.126
h6	878.728	0.250
h7	424.357	0.121
h8	432.165	0.123

Large set of plots showing, for each moment, how the landscapes are looking. Note that 'v' and 'sigma' are labelled 'h1' and 'h2' because I forgot to change the y-labels. I've also omitted the plots for the dummy moments h9 through h12 since they're all essentially 0.