 
Summary: Jazayeri & Movshon 1 Supplementary Information
A new perceptual illusion reveals mechanisms of sensory decoding
Mehrdad Jazayeri & J. Anthony Movshon
Supplementary Methods
The complete model
The complete model is composed of an encoding and a decoding stage. At the encoding
stage, it assumes the sensory representation has a Gaussian probability density function
centred at the true direction of motion. The decoding stage computes sensory likeli
hoods by multiplying the sensory representation with a weighting profile modelled as a
gamma density function. To account for the discrimination data, we assume that a bi
nomial process in which the underlying probabilities are taken from the area of the sen
sory likelihood in the clockwise (CW) and counterclockwise (CCW) parts of the result
ing sensory likelihoods governs subjects' choices. The direction estimates are modelled
as the peak of the sensory likelihood plus an additional constant term to account for any
motor bias independent of sensory evidence. Therefore, the encoding model has 3 pa
rameters representing the standard deviation of the Gaussian sensory representation for
the 3 coherence values tested (i.e. 3%, 6% and 12%), and the decoding model has 4 pa
rameters: 3 for the gamma density function and 1 for the constant bias term.
The discrimination and estimation data were simultaneously fitted to minimize the
arithmetic sum of two error terms: the negative binomial likelihood of observing the
