Approximate Recall Confidence Intervals
  Recall, the proportion of relevant documents retrieved, is an important measure of effectiveness in information retrieval, particularly in the legal, patent, and medical domains. Where document sets are too large for exhaustive relevance assessment, recall can be estimated by assessing a random sample of documents; but an indication of the reliability of this estimate is also required. In this article, we examine several methods for estimating two-tailed recall confidence intervals. We find that the normal approximation in current use provides poor coverage in many circumstances, even when adjusted to correct its inappropriate symmetry. Analytic and Bayesian methods based on the ratio of binomials are generally more accurate, but are inaccurate on small populations. The method we recommend derives beta-binomial posteriors on retrieved and unretrieved yield, with fixed hyperparameters, and a Monte Carlo estimate of the posterior distribution of recall. We demonstrate that this method gives mean coverage at or near the nominal level, across several scenarios, while being balanced and stable. We offer advice on sampling design, including the allocation of assessments to the retrieved and unretrieved segments, and compare the proposed beta-binomial with the officially reported normal intervals for recent TREC Legal Track iterations. 
William Webber
cs.IR