A Bayesian psychophysical model for angular variables

• A link of observed response distributions to the theoretical constructs from Bayesian decision theory.
• A derivation of response distributions for a normal and von Mises distribution for angular variables.
• Theoretical response distribution is always unimodal in the case of normal distributions.
• Theoretical response distribution becomes fundamentally distinguishable in the new angular setting.
• It becomes bimodal in the angular setting in the case when prior and likelihood are about equally strong.

Bayesian theories of perception provide a link between observed response distributions and theoretical constructs from Bayesian decision theory. Using Bayesian psychophysics we derive response distributions for two cases, one based on a normal distribution and one on a von Mises distribution for angular variables. Interestingly, where the theoretical response distribution is always unimodal in the case of normal distributions, it can become bimodal in the angular setting in the case when prior and likelihood are about equally strong.