Ideal observer analysis is a method for investigating how information is processed in a perceptual system.
If there is uncertainty in the task, then perfect performance is impossible and the ideal observer will make errors.
The fundamental role of uncertainty and noise implies that ideal observers must be defined in probabilistic (statistical) terms.
Das and Geisler [8] described and computed the detection and classification performance of ideal observers when the stimuli are normally distributed.
These include the error rate and confusion matrix for ideal observers when the stimuli come from two or more univariate or multivariate normal distributions (i.e. yes/no, two-interval, multi-interval tasks and general multi-category classification tasks), the discriminability index of the ideal observer (Bayes discriminability index) and its relation to the receiver operating characteristic.