[obsolete] Update sampling output window

[magland]

This is a redo of #21

I took all those changes and put them on top of the new chain of changes - since the file sharing has been revamped.

See the discussion in the other PR. I think there are still some things to check/improve, but I think it would be great to merge this for now.

[WardBrian]

I don't know much about the state of javascript testing, but I would feel a lot better if we had some tests on the ess/rhat functions at least. They're famously tricky.

For example, I just did a run where this is what is reported in the UI:

Parameter	Mean	MCSE	StdDev	5%	50%	95%	N_Eff	N_Eff/s	R_hat
lp__	17.40	0.04792	1.472	14.61	17.79	18.97	944.2	4253	1.001
accept_stat__	0.9308	0.001749	0.1099	0.7072	0.9733	1.000	3951	1.780e+4	1.021
stepsize__	0.2542	0.01212	0.02797	0.2224	0.2716	0.2906	5.330	24.01	7.127e+12
treedepth__	2.979	0.01316	0.7855	2.000	3.000	4.000	3561	1.604e+4	1.013
n_leapfrog__	10.46	0.08561	5.148	3.000	11.00	15.00	3616	1.629e+4	1.013
divergent__	0.000	NaN	0.000	0.000	0.000	0.000	NaN	NaN	NaN
energy__	-15.93	0.05853	1.897	-18.30	-16.26	-12.19	1050	4729	1.001
alpha	-0.1038	0.001918	0.06552	-0.2122	-0.1033	-0.0009766	1167	5259	1.008
beta	1.252	0.0002855	0.01058	1.235	1.252	1.270	1374	6187	1.005
sigma	0.09158	0.0008137	0.02854	0.05753	0.08598	0.1465	1230	5541	1.003

Downloading the draws and then splitting into four csvs before feeding to stansummary produces

Parameter	Mean	MCSE	StdDev	5%	50%	95%	N_Eff	N_Eff/s	R_hat
lp__	1.73637e+01	4.57725e-02	1.45807e+00	1.44671e+01	1.77336e+01	1.89540e+01	1.01473e+03	inf	1.00543e+00
accept_stat__	9.20493e-01	2.70119e-02	1.37043e-01	6.45094e-01	9.73256e-01	1.00000e+00	2.57397e+01	inf	1.05173e+00
stepsize__	2.66687e-01	4.07137e-02	5.76645e-02	1.91289e-01	2.61945e-01	3.53548e-01	2.00602e+00	inf	6.53902e+13
treedepth__	3.02475e+00	9.96645e-02	8.10741e-01	2.00000e+00	3.00000e+00	4.00000e+00	6.61734e+01	inf	1.02400e+00
n_leapfrog__	1.07520e+01	8.12053e-01	5.61590e+00	3.00000e+00	1.10000e+01	1.50000e+01	4.78268e+01	inf	1.03143e+00
divergent__	0.00000e+00	nan	0.00000e+00	0.00000e+00	0.00000e+00	0.00000e+00	nan	nan	nan
energy__	-1.58774e+01	5.88228e-02	1.92866e+00	-1.82709e+01	-1.62244e+01	-1.21951e+01	1.07503e+03	inf	1.00534e+00
alpha	-1.00380e-01	1.89720e-03	6.60711e-02	-2.07514e-01	-1.00932e-01	8.42572e-03	1.21281e+03	inf	1.00103e+00
beta	1.25135e+00	3.10310e-04	1.06537e-02	1.23415e+00	1.25148e+00	1.26825e+00	1.17871e+03	inf	1.00139e+00
sigma	9.19273e-02	8.43256e-04	2.92637e-02	5.75119e-02	8.51957e-02	1.47602e-01	1.20432e+03	inf	1.00410e+00

Ideally these would agree. I think a package which implemented these MCMC diagnostics and tested them against Stan's implementation would be a great service to the broader ecosystem, so it is probably worth pulling them out

[magland]

@WardBrian I agree. I propose we first make sure everything is good in bayes_kit in Python, and then match it exactly in .js, with tests. I did this with ess_imse for mcmc-monitor and ported the code over to stan-playground. But I'm sure it needs to be revisited (IDK if bayes_kit was finalized at that point)

[WardBrian]

Momentum on the bayes-kit project has pretty much stalled. The tests in Stan's C++ have also been used in e.g. the Rust mcmc package, but porting them to this environment may be a bit annoying

[magland]

replaced by #46