cmbchisq should not be combined when two detectors are experiencing different noise profiles
Our combination of chisq from each detector has some issues.
We essentially take the average of the reduced chisq between each detector. This works in theory, but in practice, there are some edge cases to consider.
The point of SNR and Chisq is to distinguish between astrophysical signals and noise. In general:
- Gaussian noise typically has low SNR and low-moderate Chisq
- Astrophysical signals will have high SNR and ~1 chisq
- Glitches are often characterized by both high SNR and high Chisq.
If two detectors are following a different profile, the combination of their chisq may make result in the trigger moving from one profile to another.
e.g. If Hanford sees a glitch with chisq 4 while Livingston sees low gaussian noise with chisq 0.25, the resulting cmbchisq would be ~2.1.
For the most part, we use upload criteria to prevent these cases. At least two detectors must have chisq between 0.3-3, and no detector may have a chisq less than an 8th of another detector. There are a couple of other checks, e.g. on sngl FAR, though the chisq checks are the most substantial.
These flat thresholds are not foolproof. We've had 2 retractions as a result of unreasonable chisq. In addition, they're not scalable as more detectors are added to the network.
Relatedly, see #49. It describes a separate issue with cmbchisq. In short, we should have been adding the non-reduced chisq, then reduced the cmbchisq by the sum of the degrees of freedom of each sngl chisq. The difference is reasonably small however, considering that we use the same chisq length for each detector.