So, it seems that the debinning function has a couple of nasty flaws:
Whenever the probability is high, the noise in the debinning function is
high, proportional to the number of (expected) points. If I uniformly reduce
the number of expected points, I also smooth out any signal. Also, setting
nEx artificially imposes a parameter (grr...)
The covariance knows that the debinning function is guaranteed to be normalized.
Thus, using the covariance in any meaningful way gives a very interesting
result of zero, modulo the noise mentioned above. However, using only the
variance in some tricky way feels like cheating.
Two ideas for the noise:
- Punish noise proportionally to probability. Hopefully, in a parameterless way.
- Somehow build in subtraction to the debinning function. Hopefully, without losing cool properties of the debinning function.