Assessing the accuracy of estimates of the likelihood ratio

There are many methods to estimate, from ensembles of signal-present and signal-absent images, the area under the receiver operating characteristic curve for an observer in a detection task. For the ideal observer on realistic detection tasks, all of these methods are time consuming due to the difficulty in calculating the ideal-observer test statistic. There are relations, in the form of equations and inequalities, that can be used to check these estimates by comparing them to other quantities that can also be estimated from the ensembles. This is especially useful for evaluating these estimates for any possible bias due to small sample sizes or errors in the calculation of the likelihood ratio. This idea is demonstrated with a simulation of an idealized single photon emission detector array viewing a possible signal in a two-dimensional lumpy activity distribution.