A framework for Bayesian optimality of psychophysical laws

The Weber-Fechner law states that perceived intensity is proportional to physical stimuli on a logarithmic scale. In this work, we formulate a Bayesian framework for the scaling of perception and find logarithmic and related scalings are optimal under expected relative error fidelity. Therefore, the Weber-Fechner law arises as being information theoretically efficient under the constraint of limited representability. An even stronger connection is drawn between the Weber-Fechner law and a Bayesian framework when neural storage or communication is the dominant concern, such as for numerosity. Theoretical results and experimental verification for perception of sound intensity are both presented.