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.

► Psychophysical scales arise as informational optimizations under neural constraints.
► Two quantization-theoretic models of perception are developed.
► Weber–Fechner law minimizes expected relative error for natural stimuli in the first.
► Weber–Fechner law minimizes expected relative error for all stimuli in the second.
► Experimental verification for perception of sound intensity is presented.