Continuing from yesterday, I continued to run some simulations to see whether Gaussian data sets could ever be completely sigma-clipped away. I did this for sigma-clipping of 2.75, 2.5, and 1.0, before eventually deciding that if we include the measurement error in the sigma-clip parameters there is absolutely no way to remove all of the data. The measurement error on some of the points was way larger than the standard deviation of the entire sample, so those data points were almost never removed by the sigma-clipping.
The rest of the day (at least until now) was spent learning about the KMM algorithm, which can be used to detect bimodality in data samples. Bimodality means that there are two peaks in the sample, which for astronomical data typically means that there are two stellar populations in the sample. This can be used to detect multiple galaxies or star clusters or just stars from the same population!
The cool thing about the algorithm is that it can detect bimodalities in samples that appear somewhat single-Gaussian to the naked eye when put into a histogram. But it's not perfect and works best when both samples have the same standard deviation, something which I believe to be rather unlikely in the real world. But it still gives a decent indication that something other than a single population is in the sample.