LIGO Document G1500977v2
 A common problem in inference is the estimation of the efficiency of some process using the results of a finite set of Bernoulli trials (experiments with two possible outcomes, e.g., success and failure), and to use those efficiency estimates to assign a probability of success to future or hypothetical experiments. For example, we may wish to estimate the detection efficiency of a pipeline given a set of detected and nondetected simulated signals. The problem is complicated if the trials are not identical, but depend on some properties (e.g., simulated signal strength) which differ from trial to trial, and we wish to obtain an efficiency as a function of those properties. I will review the Bayesian approach to this problem, which uses the full set of observed results, without binning, to make inferences about the efficiency, and describe its application to the results of the recent Scorpius X1 Mock Data Challenge.

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