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1. Introduction And Scope
Signal detection theory (SDT) sprouted from World War II research on radar into a probability-based theory in the early 1950s. It speciﬁes the optimal observation and decision processes for detecting electronic signals against a background of random interference or noise. The engineering theory, culminating in the work of Wesley W. Peterson and Theodore G. Birdsall (Peterson et al. 1954), had foundations in mathematical developments for theories of statistical inference, beginning with those advanced by Jerzy Neyman and E. vs. Pearson (1933). SDT was taken into psychophysics, then a century-old branch of psychology, when the human observer’s detection of weak signals, or discrimination between similar signals, was seen by psychologists as a problem of inference. In psychology, SDT is a model for a theory of how organisms make ﬁne discriminations and it speciﬁes model-based methods of data collection and analysis. Notably, through its analytical technique called the receiver operating characteristic (ROC), it separates sensory and decision factors and provides independent measures of them. SDT’s approach is now used in many areas in which discrimination is studied in psychology, including cognitive as well as sensory processes. From psychology, SDT and the ROC came to be applied in a wide range of practical diagnostic tasks, in which a decision is made between two confusable alternatives (Swets 1996).
2. Electronic Detection And Statistical Inference
Central to both electronics and statistics is a conception of a pair of overlapping, bell-shaped, probability (density) functions arrayed along a unidimensional variable, which is the weight of evidence derived from observation. In statistical theory, the probabilities are conditional on the null hypothesis or the alternative hypothesis, while in electronic detection theory they are observational probabilities conditional on noise-alone or signal-plus-noise. The greater the positive weight of evidence, the more likely a signal, or signiﬁcant experimental eﬀect, is present. A cutpoint must be set along the variable to identify those observed values above the cutpoint that would lead to rejection of the null hypothesis or acceptance of the presence of the designated signal. Errors are of commission or omission: type I and type II errors in statistics, and false alarms and misses in detection. Correct outcomes in detection are hits and correct rejections. Various decision rules specify optimal cutpoints for diﬀerent decision goals. The weight of evidence is unidimensional because just two decision alternatives are considered. Optimal weights of evidence are monotone increasing with the likelihood ratio, the ratio of the two overlapping bell-shaped probability functions. It is this ratio, and not the shapes of the functions, that is important.
3. Modern Signal Detection Theory
In the early 1950s, Peterson and Birdsall, then graduate students in electrical engineering and mathematics, respectively, at the University of Michigan, developed the general mathematical theory of signal detection that is still current. In the process they devised the ROC—a graphical technique permitting measurement of two independent aspects of detection performance: (a) the location of the observer’s cutpoint or decision criterion and (b) the observer’s sensitivity, or ability to discriminate between signal-plus-noise and noisealone, irrespective of any chosen cutpoint. The two measures characterize performance better than the single one often used, namely, the signal-to-noise ratio (SNR) expressed in ener