Figure 5.

The discrimination parameter σ is undetermined. (a) Graph of an example log prior, log p_θ(θ) (solid horizontal sinusoid curve), as a function of lighting direction θ. Given two hypothetical neurons with preferred lighting directions θ and $\overline{\theta }$, their responses are determined by their log probability density functions, log p(θ) and $\text{log}p(\overline{\theta })$, indicated by the vertical dashed and solid curves, respectively. For a given stimulus, the larger of the two observed values from the probability density functions log p(θ) and $\text{log}p(\overline{\theta })$ determines the lighting direction assumed by the observer, and this, in turn, determines the concave/convex observer response. These two observed values are noisy estimates of the probability density function means, so the choice probability q (see equation (2.19)) is determined by the relative overlap of the probability density functions (vertical dashed and solid curves) for these two quantities. (b) A log prior with amplitude variations k times smaller than in (a) leads to the same choice probabilities as in (a), provided the noise level σ is also reduced by a factor k. (For simplicity, this analysis assumes a concavity preference of 0.5.)