Ideas

Short essays on one question: how to sort events into a few bins without throwing away what they say about the parameters being measured. Each takes one idea and one picture, and assumes basic statistics but nothing about ScoreQuant. They are best read in order.

1. Bin by score, not by feature. Binning loses exactly the scatter of the score inside each bin, so the bins belong in score space.
2. Why k-means is the wrong clustering for D. k-means adds up what each direction keeps; D-optimality multiplies it.
3. When Lloyd goes backwards. The k-means recipe, borrowed for D-optimality, can make the bins worse. Moving one event at a time cannot.
4. Nuisance parameters break the rule. With a nuisance parameter fitted alongside, the best bins no longer contain a rule for new events.
5. How much did my binning keep? One ratio, and the three questions that decide how far to trust it.

The walkthroughs carry the same ideas through four complete problems.