Statistical inference on recall, precision and average precision under random selection

The objective of a rare target detection problem is to identify the rare targets as early as possible. Recall, precision and average precision are three popular performance measures for evaluating different detection methods. However, there is little literature on the statistical properties of these three measures. We develop a framework for conducting statistical inference on recall, precision and average precision through establishing their asymptotic properties. Simulations are used to illustrate the idea. The proposed methods can also be applied in other areas where ranking systems need to be evaluated, such as information retrieval.