Generalization of the Theory of Signal Detectability ton-Eventm-Dimensional Forced-Choice Tasks

This paper presents a generalization of the theory of signal detectability ton-event forced-choice tasks where the evidence can be modelled by anm-dimensional vector. The generalization is based on a nonparametric model that encompasses decision rules for maximizing the proportion of correct decisions. The model assumes that observers identify events by partitioning a decision space of dimensionn−1 with a template. Translating the template by varying the decisional bias yields a set of receiver operating characteristic (ROC) surfaces. Following B. K. Scurfield [1996,J. Math. Psych.40, 253–269], event-discriminability is defined by considering the Shannon entropy of the volumes under the ROC surfaces. The resultant discriminability measure is interpreted with respect to the random vectors assumed to be associated with the decision space and shown to equate with the channel capacity of an observer in a multiple-interval forced-choice task.