Supplementary Fig. 4: An illustration of the ideal observer model.
From: Perceptual bias reveals slow-updating in autism and fast-forgetting in dyslexia
The prior is set to be a uniform distribution. Bottom → up: given a true stimulus f1, noisy encoding leads to its \(\tilde f_1\) representation. For a fixed representation \(\tilde f_1\), combining sensory uncertainty \(p\left( {\tilde f_1|f_1} \right)\) with prior expectations \(\hat p\left( {f_1} \right)\) on frequency leads to the posterior \(\hat p\left( {f_1{\mathrm{|}}\tilde f_1} \right)\), and its median \(\hat m_1\left( {\tilde f_1} \right)\) is used as a threshold to form a decision. Considering all possible noisy representations leads to a distribution over the posterior median \(p\left( {\hat m_1|f_1} \right)\). Relative noise, standard deviation, and prior width were chosen to best illustrate the implementation.
