I discussed the many advantages or probability estimation over classification. Here I discuss a particular problem related to classification, namely the harm done by using improper accuracy scoring rules. Accuracy scores are used to drive feature selection, parameter estimation, and for measuring predictive performance on models derived using any optimization algorithm. For this discussion let Y denote a no/yes false/true 0/1 event being predicted, and let Y=0 denote a non-event and Y=1 the event occurred.
Imagine watching a baseball game, seeing the batter get a hit, and hearing the announcer say “The chance that the batter is left handed is now 0.2!”
No one would care. Baseball fans are interested in the chance that a batter will get a hit conditional on his being right handed (handedness being already known to the fan), the handedness of the pitcher, etc. Unless one is an archaeologist or medical examiner, the interest is in forward probabilities conditional on current and past states.