Magnitude Estimation with Noisy Integrators Linked by an Adaptive Reference

Judgments of physical stimuli show characteristic biases; relatively small stimuli are overestimated whereas relatively large stimuli are underestimated (regression effect). Such biases likely result from a strategy that seeks to minimize errors given noisy estimates about stimuli that itself are drawn from a distribution, i.e., the statistics of the environment. While being conceptually well described, it is unclear how such a strategy could be implemented neurally. The present paper aims toward answering this question. A theoretical approach is introduced that describes magnitude estimation as two successive stages of noisy (neural) integration. Both stages are linked by a reference memory that is updated with every new stimulus. The model reproduces the behavioral characteristics of magnitude estimation and makes several experimentally testable predictions. Moreover, the model identifies the regression effect as a means of minimizing estimation errors and explains how this optimality strategy depends on the subject's discrimination abilities and on the stimulus statistics. The latter influence predicts another property of magnitude estimation, the so-called range effect. Beyond being successful in describing decision-making, the present work suggests that noisy integration may also be important in processing magnitudes.