Weber's law and natural inference

For most extensive sensory variables such as speed or numerosity, the discrimination thresholds of human subjects are proportional to the value around which the discrimination is performed, a scaling known as Weber's law. Many theories have been proposed for this law, which all rely on the assumption that neurons are noisy. By contrast, we argue here that noisy neurons are not required to explain Weber's law. Instead, we propose that it is the unavoidable consequence of the statistics of natural sensory inputs. In natural environments, sensory measurements are typically scaled by global variables such as contrast in vision or loudness in audition. These global scaling parameters induce positive correlations among measurements which in turn lead to Weber's scaling. This theory makes testable experimental predictions and accounts for the fact that tuning curves to speed and numerosity in vivo are approximately log normal.