Raise the Bar

A spam filter outputs P(spam|x) from a trained logistic regression model. If you raise the decision threshold for flagging spam from 0.5 to 0.75 without retraining, what typically happens?

The model becomes non-convex and must be retrained from scratch

Fewer emails get flagged as spam; precision tends to rise while recall tends to fall

More emails get flagged as spam; recall tends to rise while precision tends to fall

Nothing changes, since the underlying probabilities are unaffected by the threshold