Optimality of decision rules in human audio/visual signal detection

The theory of signal detection in psychology and the theory of optimal signal detection in statistical theory are compared. Differences between the two are often thought to be inconsequential. However, under a close analysis, this turns out not to be true. A basis for empirical tests is some results in distribution theory. These are used to characterize the kind of linear additive model that is most consistent with the data, which suffices to discriminate between several different decision processes. Once this choice is made, the theorist obtains a model that predicts both the detection decision and the feeling of confidence that accompanies it.<>