Approximations to ideal-observer performance on signal-detection tasks.

The ideal-observer performance, as measured by the area under the receiver's operating characteristic curve, is computed for six examples of signal-detection tasks. Exact values for this quantity, as well as approximations based on the signal-to-noise ratio of the log likelihood and the likelihood-generating function, are found. The noise models considered are normal, exponential, Poisson, and two-sided exponential. The signal may affect the mean or the variance in each case. It is found that the approximation from the likelihood-generating function tracks well with the exact area, whereas the log-likelihood signal-to-noise approximation can fail badly. The signal-to-noise ratio of the likelihood ratio itself is also computed for each example to demonstrate that it is not a good measure of ideal-observer performance.