I finally found some time to read the LIGO paper. A couple things that I thought were interesting:

The peak power from gravitational waves was 200 solar masses per second. The power didn’t stay there for very long since a total of 3 solar masses was radiated away.

The rate of false positives the size of the signal seen is one in tens of thousands of years, so this is a signal that is enormously above any known backgrounds.

LIGO also uses some complicated template fitting routine where they compare the measured signal to a library of pre-calculated theoretical curves. This only gives approximate results for physics parameters, so they then have to supplement this with an actual fit.

The next biggest event had a false positive rate of only one every few years