Time-dependent Poisson counter models of response latency in simple judgment

An important class of sequential-sampling models for response time (RT) assumes that evidence for competing response alternatives accrues in parallel and that a response is made when the evidence total for a particular response exceeds a criterion. One member of this class of models is the Poisson counter model, in which evidence accrues in unit increments and the waiting time between increments is exponentially distributed. This paper generalizes the counter model to allow the Poisson event rate to vary with time. General expressions are obtained for the RT distributions for the two- and the m-alternative cases. Closed-form expressions are obtained for response probabilities under a proportional-rates assumption and for mean RT under conditions in which the integrated event rate increases as an arbitrary power of time. An application in the area of early vision is described, in which the Poisson event rates are proportional to the outputs of sustained and transient channels.