Signal detection theory

Bayes rule, Eq. (3-164), finds many applications in problems of statistical inference86 and signal detection theory,36 where the conditional probability on the right can be calculated directly in terms of the physical parameters of the problem, but where the quantity of real interest is the conditional probability on the left. 

In signal detection theory such mistakes are considered to be the logical consequence of the fact that the normal distribution of the sensation caused by the noise alone and that of the sensations caused by signal plus noise overlap to a considerable degree (see figure 1). 

Signal detection theory supposes that the subject, when faced with this situation, sets... 

Signal plus Noise (S+N) according to Signal Detection Theory. Three hypothetical response criteria (Cj, C2 and C3) set by the subject are indicated. 

Another methodological consequence can be inferred from signal detection theory as well. 

Egan, J. P. (1975) Signal detection theory and ROC analysis, Academic Press, New York. 

The experiments with H. M. employed a battery of tests. One set of experiments measured his sensitivity by means of a technique derived from signal detection theory (Corbit Engen, 1971), in which I asked H. M. to sniff 20 presentations of dilute odorant solution randomly interspersed with 20 presentations of odorless blank. The odor was so faint as to make it hard to tell it apart from blank. Figure 1 compares some of the data for H. M. with a male normosmic (P. D.) matched for age and race. After each presentation I asked H. M. whether he could smell an odor. His pattern of responding was the same as that of normosmics sometimes he gave affirmative responses to blanks (false alarms, symbolized by open symbols in fig. 14.1), but he did not always respond affirmatively to the dilute sample (correct affirmatives are symbolized by solid symbols in fig. 14.1). 

Swets, J.A., and Pickett, R.M. Evaluation of Piagnostic Systems. Methods from Signal Detection Theory Academic Press Hew York, 1982 Chapter 1. 

Green, D. M., and Swets, J. A (1988), Signal Detection Theory and Psychophysics, John Wiley Sons, New York. 

McNichol, D. (1972), A Primer of Signal Detection Theory, Allen Unwin, London. 

From the classical perspective, the decision maker is concerned with determining the likelihood that a hypothesis is true. Bayesian inference is the best-known technique, but signal detection theory, and fundamentally different approaches such as the Dempster-Schafer method, have seen application. Each of these approaches is discussed below. 

TABLE 4 Potential Outcomes Considered by Signal Detection Theory... 

Lehto, M. R., and Papastavrou, J. (1991), A Distributed Signal Detection Theory Model Implications to the Design of Warnings, in Proceedings of the 1991 Automatic Control Conference (Boston), pp. 2586-2590. 

Lehto, M.R. and J.D. Papastavrou (1998). A signal-detection theory based perspective on design of warning. Perceptual and Motor Skills 86 (2) 720-722. 

Errors in problem detection (see also signal detection theory)... 

Figure 8 The decision space for signal detection theory, which has received support both in general [33,34,41] and in the detection of odors [55,135]. According to one common version of the theory, both blank and odorant give rise to Gaussian distributions of sensory strength with equal variance. The subject responds yes if an observed value of sensory strength exceeds some criterion (dashed vertical line), and no otherwise. The area under each distribution to the right of criterion corresponds to the probability the observer will respond yes to a given stimulus correct responses hits ) for odorants and incorrect responses false alarms) for blanks. Empirical estimates of these probabilities allow one to calculate the distance between the means of the two distributions in units of their common standard deviation, termed d d (which equals 2 in this case) remains constant as criterion changes (see Ref. [41] for an excellent overview).

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