Yesterday I slightly refined my code to also create a summary .pe file. This file also includes the k's, but includes the weights and means and variances of the predicted components. Thus when it detects two populations it is pretty easy to see if the second Gaussian has a small fraction of the total number of stars. If it does, it's probably caused by an outlier and shouldn't be viewed as significant.
Most of today was spent attempting to extract the actual Bootes II data from the data set. This was complicated by the fact that (as I realized after some time) some of the data points were duplicates, and some were just ridiculous and shouldn't even be counted. But with Beth's help I was finally able to narrow the 243 stars down to the 21 that are actually supposed to be in the galaxy. I then did my typical bootstrap/Nmix analysis.
But first I ran Nmix on the actual data, with the following results:
Bootes II Nmix Results
1) 21.3% confidence in 1 component, with mean of -122.9
2) 18.9% confidence in a 2 component fit, with means of -128.5 and -114.58
3) 14.2% confidence in 3 components
4) 10.4% confidence in 4 components
So these results are rather ambiguous, with no really obvious number of components. But that is probably a result of the small sample size of 21 stars. This is the least confident of all of the samples I have tested so far.
Bootes II Bootstrap Nmix Results
1) Only 15% had above 10% confidence for a single population, 5% above 20%
2) 25% of both the 2 and 3 component fits had a confidence above 10%
3) 10% had a 2 component fit with confidence above 20%, 5% of the 3's
4) However, in one of the 2 component best-fits where there was no chance of a single peak, 83% were in one of the peaks. Not sure where to make the cutoff that says the other peak is insignificant.
Overall, this was ridiculously inconclusive, but 2 components seems to win out.
1) Learn more about bootstrapping/jack-knifing
2) Make a code that will read the Nmix data, then determine if the multi-component fit is significant or not based on the relative weights