  Postselection is the process of discarding outcomes from statistical trials
that are not the event one desires. Postselection can be useful in many
applications where the cost of getting the wrong event is implicitly high.
However, unless this cost is specified exactly, one might conclude that
discarding all data is optimal. Here we analyze the optimal decision rules and
quantum measurements in a decision theoretic setting where a prespecified cost
is assigned to discarding data. Our scheme interpolates between unambiguous
state discrimination (when the cost of postselection is zero) and a minimum
error measurement (when the cost of postselection is maximal). We also relate
our formulation to previous approaches which focus on minimizing the
probability of indecision.
