(1) Experimental method: There are a variety of experimental procedures for measuring the detectability or discriminability of stimuli. Some are subject to bias and nothing can be done about it. The signal-detection task with catch trials is subject to bias, but one can estimate both bias and discriminability from the resulting data. 2-interval forced-choice procedures are arguably bias-free.

(2) Theory: All sensory measurements are corrupted by noise, i.e., are variable. It is useful to compare human performance to that of an ideal observer who optimally combines the sensory information and makes a decision that accounts for prior information, noisy sensory information, and the costs and benefits of various outcomes of the decision. The principle: Bayesian decision theory.

(3) Specific case: Standard signal detection theory is identical to Bayesian decision theory in which all the evidence used for a binary task (detection or discrimination) is summarize as a single number, the decision variable, which is on average low for one stimulus (the blank, or noise-alone trials) and high for the other (the stimulus-plus-noise trials). For this case, the ideal observer adopts a specific criterion value of the decision variable, and says "Yes, it's a signal trial" whenever the decision variable exceeds that criterion. From data in a yes-no task with catch trials we can estimate bias (the criterion value) and discriminability (d-prime, the difference between the means divided by their common variance).

(4) Applications: This theory may be applied to any detection or discrimination task. In some cases, we can identify all the sources of noise, for example the case of detecting a very weak, brief pulse of light, which is dominated by noise in the stimulus (Poisson statistics of photons). But the theory is useful in any situation with variable binary judgments, from studies of memory (visual short-term memory, list-learning, etc.) to the effects of selective attention, etc.