HinLeung622
commented
3 years ago @grd349
Results for relaxing the priors on mean Av and spread Av came out. The current priors are:
mean Av ...............~ beta(1.1,1.1)*0.2 #0.0 to 0.2
spread Av ............~ lognormal(log(0.01), 1.0)
For 5000 turning and 1000 sampling steps:
Immediately it is clear that the less informative priors on Av have gave rise to instable Rhats. The mean Av estimate increased from roughly 0.13 to now 0.16, going from being in line with the GAIA OC paper (0.13) and DBossini (0.11) to be in line with Green's 2019 dustmap (0.16).
Secondly, the spread Av estimate widened from roughly 0.01 to 0.03. This widened the width of the main sequence of red dots in the CMD. Though it is reassuring to see that the increased width of the Av distribution did not overlap with the binary track, meaning the red dots are still localized to the MS track, and the binary stars are still modelled with the mixture model.
Thirdly, the width of the estimated observational G mag error went down from 160 to 105, most likely due to the larger spread Av. This means the singular distribution in the mixture model (last plot) is thinner.
If you think the estimates on mean and spread Av are physical, I think this is again just a convergence problem, which just means putting on more tuning steps.
Exciting results:
grd349
Problem is, when I plot what my NNs expect stars from 0.8 to 1.2 Msun would look like given Ruprecht 147 literature values for fundamentals next to the data dots:
Yeah, I think we will have to ditch Ruprecht 147
It's great to see relatively lower Rhats, especially in dist_mod and zero_pt. The corner plot is also much more well defined. The age stays lower than literature values. I am waiting on runs of M67 with a large number of tuning steps.
Ignoring the high Rhats (i only put on 5000 tuning steps to test the coarse features), the age estimate has moved from 3.1Gyr to now 2.1 Gyr, again pushing right up against the lower age prior. Similar situation appears with the mean Av estimate: 0.19 when the prior max is 0.2. This is likely why the previous Av estimates were at 0.16, a value higher than GAIA's estimated 0.11 value.
testings with the CMD also shows the same story:
4.0Gyr + 0.11 Av
2.0Gyr + 0.19 Av
Perhaps we need some stars at the turn off to better constraint this degeneracy. Though that runs into the 1.2Msun overshooting limit. Maybe we could somehow constraint Av with another set of observables (another band?). Thoughts?
First of all, the addition of K band data did not fix the low age problem. It might have broken the age-Av degeneracy considering the mean Av estimate here is ~0.15, quite a bit lower than the 0.19 I got previously when the age came out to be ~2.1. Age might be degenerate with something else now. Here is a corner plot (it is very large so you might have to download/view image in a separate tab to see it properly):
Secondly, the dist_mod estimate is very low. Gaia determines M67's dist mod to be ~9.72, most previous HBM runs result in estimates within 9.70 to 9.75. I tested that this is not the result of a mistake I made when changing the treatment of the zero pt offset by plotting the predicted M67 MS (the red chain of circles I sometimes show overlapped with the blue data dots) using dist_mod=9.53 vs dist_mod=9.72, and under the sets of estimated parameters in this HBM run, dist_mod=9.53 really does fit the data's MS more under visual inspection. I am not sure what caused this problem.
Constraining the prior on spread Av to be closer to 0 certainly will help this situation, but I don't think that is proper practice. I really am not sure.
With some annotation:
Note: zeropoint offset is omitted
test6 = the old NN without Ks band and higher biases
atmos2BC_withK4_1 = the new NN with Ks band and lower biases
The new NN did introduce a clockwise rotation to the predicted values, which disagrees with data.
good convergence, but age is very low (2.06) with small uncertainty (0.046). Av is very low (0.048) and MLT is very low (1.74) but somehow this combination of fundamentals is able to give a CMD that agrees with the data:
Seeing the strange Av values and MLT, I decided to help the sampler with very informative priors on Y, MLT and Av, meaning only age, dist_mod and feh are on the same uninformative priors as before:
great convergence, but age is still low (2.34) despite fixing a lot of stuff already. The feh went a bit high, so I decided to fix feh and additionally dist_mod as well:
And so with super informative priors on everything but age and mass, without binary stars that require a fancy mixture model, without Av spread, the estimated age is 2.9Gyr with a very small uncertainty (0.032). I have no idea why the sampler keep preferring a lower age to higher age when in theory both should fit the data equally well (if we are assuming age has little effect to the MS). My only thought is that the matching set of masses of a lower age results in a MS slope that is more comparable to the data, while that of a higher age disagrees more, so the sampler favours a low age?
This is a continuation of issue #47 . A new thread is made since the last one is getting ridiculously long and it takes ages to load in all the images.
State of the HBM: data = M67 low mass dwarfs with binaries/double stars included (total = 354 stars) + the cluster-average-parallax from GAIA https://arxiv.org/pdf/1804.09378.pdf + the surface metallicity of 10 MS stars from https://iopscience.iop.org/article/10.3847/1538-4357/aab612
full model: 2x working versions, one with max pool MLT, one with partial pool MLT. The max pool MLT:
with priors: mean age ............~ beta(2,2)2+3 mean feh .............~ beta(2,2)0.3-0.15 mean Y .................~ beta(2,2)0.0334+0.2466 #0.24668 \pm 0.00007 is big bang nucleosynthesis fraction from Plank mission mean MLT ...........~ beta(10,10)0.6+1.7 #whole range of MLT in training grid mass ......................~ beta(1.1,1.1,shape=N)0.4+0.8 #0.8 to 1.2 mean Av ...............~ beta(1.1,1.1)0.2 #0.0 to 0.2 spread Av ............~ lognormal(log(0.01), 1.0) dist_mod .............~ N(9.726, 1.0) #9.726 is taken from the GAIA DR2 cluster paper zero_pt .................~ N(-82, 33) #in micro arc seconds, from https://ui.adsabs.harvard.edu/abs/2018ApJ...862...61S/abstract q ..............................~ beta(1.1,1.1) delta_mG .............~ lognormal(log(0.3), 0.4) f ...............................~ lognormal(log(10), 0.7) sigma_multiple ..~ lognormal(log(0.3),0.3)
The max pool MLT case assumes a MLT dependency on star mass, has these additional elements:
Current best run results: with 20000 tuning steps and 1000 sampling steps (with tighter mean Av and spread Av priors):
The remaining problem is the high Rhats and low effective sample size in dist mod and zero pt (see #49 )
Partial MLT works except for again, the problems with dist mod and zero pt. The estimated slope of MLT against mass is very slightly negative, suggesting no need for partial pooling MLT.