BDT scores: Signal vs Background

[ChrisVer]

I have one question:
Many times, in order to test whether an outcome should be considered as "Signal" (S) or "Background" (B), we are using BDTs which we have trained on known outcomes...
I was wondering though, the outcome of being S/B is binary : either it's signal or it's not... the only way I can interpret the BDT variable after that is as "how likely it is to be signal or not", since a particular cut on the BDT corresponds to some particular background rejection and signal efficiency (ROC curves).
Is my interpretation correct? Would a "signal" object with a BDTscore=0.89 be a less likely signal than one with BDTscore=0.95 ? If not, then is there a way to compare the two events? I.e. the higher I place a cut on BDT the stronger/tighter signal events I'm selecting?

 

[mfb]

the outcome of being S/B is binary

It doesn't have to be. You can make multiple categories with increasing S/B ratio (increasing BDT score) and study them separately. LHCb does this for $B_s \to \mu \mu$ measurements, ATLAS and CMS do this for $H \to \gamma \gamma$ measurements for example. It improves your sensitivity compared to a single cut.

 

[ChrisVer]

It doesn't have to be. You can make multiple categories with increasing S/B ratio (increasing BDT score) and study them separately. LHCb does this for $B_s \to \mu \mu$ measurements, ATLAS and CMS do this for $H \to \gamma \gamma$ measurements for example. It improves your sensitivity compared to a single cut.

Sorry I didn't mean the ratio between Signal and Background, but being Signal or being Background (shortly I wrote S/B for S or B)

 

[mfb]

I know, but what the BDT gives you is a ranking in terms of S/B ratio.