Performance measures for dynamic signal detection

Abstract

For more than half a century, experimental studies of various kinds of detection and discrimination behavior have tended to rely on the simple, two-stage statistical decision model known as signal detection theory. An apparent weakness of this classical framework is its assumption that making a decision is equivalent to choosing a decision criterion or boundary to map perceptual or evidence states to a binary classification response. This static representation leads to several fundamental mispredictions about qualitative properties of discrimination, each of which is characteristic of a dynamic detection process. In this article, we show that there is a robust solution to a second class of problems introduced originally by detection theorists, but later mostly abandoned — the problem of estimating the detectability of the signal when the decision process is sequential. In an empirical application, a detectability statistic defined on a crude description of the temporal dynamics of the detection process is shown to be roughly constant under manipulations of both response preference and response speed. The estimated stringency of the stopping condition decreased in conjunction with a decrease in signal strength in time, consistent with the hypothesis that sensory information is retrieved from a decaying memory store. The analysis also makes it possible to estimate the bivariate distribution of the sensory and non-sensory components of the response time.