Cost of postselection in decision theory
Abstract
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.
Keywords
Cite
@article{arxiv.1504.03740,
title = {Cost of postselection in decision theory},
author = {Joshua Combes and Christopher Ferrie},
journal= {arXiv preprint arXiv:1504.03740},
year = {2015}
}
Comments
V1: 9 pages, 9 figures and one coffee stain. V2: new title and some minor improvements. One major change ... the coffee stain leaked further