A framework for Bayesian optimality of psychophysical laws

John Z. Sun, Grace I. Wang, Vivek K. Goyal, Lav R. Varshney

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)495-501
Number of pages7
JournalJournal of Mathematical Psychology
Issue number6
StatePublished - Dec 2012
Externally publishedYes


  • Bayesian Quantization
  • Psychophysical Scale
  • Relative Error
  • Weber-Fechner

ASJC Scopus subject areas

  • Psychology(all)
  • Applied Mathematics


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