On a class of additive learning models: Error-correcting and probability matching

A general model for learning signal detection in a Yes-No task is considered in which (a) the decision criterion shifts upward and downward by equal steps, and (b) the probability that the criterion shifts on a trial depends on the stimulus-response pair on that trial. Conditions are given for this process to have a unique stationary distribution, and the behavior of the process, as the step-size decreases to zero, is studied. The special model where criterion shifts may occur only on error trials can account for the probability matching behavior and for the interaction between signal strength and signal probability typically observed when the payoff matrix is symmetrical. Further, when the shift probability is assumed to be an increasing function of the distance of the sensory input from the criterion, the stationary mean criterion values are less extreme than the values that yield probability matching. It is shown that the model provides a way of incorporating payoff matrix asymmetry. Finally, the standard error in the maximum likelihood parameter estimates is calculated and a statistic is proposed for discriminating the error-correcting model from the more general model.