Signal-detection with d′≡0d′≡0: A dynamic model for binary prediction

Asymptotic performance in a binary prediction experiment can be accurately modelled with a Markov chain (e.g., from stimulus sampling theory), as also can the approach to that asymptote, but not–not  –with the same parameter values. Instead, a signal-detection model is proposed with d′d′ set equal to zero. Performance in signal detection experiments fluctuates from trial to trial, and the principal thesis of this article is that the fluctuations at asymptote in binary prediction are of the same psychological nature as in signal detection. The asymptotic behaviour in both kinds of experiment is accommodated by a large displacement of the criterion, up or down the model axis, following each error or failure of prediction. The slow rate of convergence to asymptote is accommodated by a drift of the criterion from one trial to the next. In addition, the criterion varies, not only from trial to trial, but also between different participants subsumed in the one body of data. This signal detection model enables binary prediction to be related to a broader class of experimental tasks and the model assumptions justified by reference to existing signal-detection experiments (with d′>0d′>0). Binary prediction is presented here as a stochastic process that converges to a dynamic equilibrium. ‘Learning’ equates to the convergence of decision criteria to that equilibrium and participants need otherwise have no knowledge of the schedule of outcomes.