The size-weight illusion and beyond: A new model of perceived weight
Fig 6
Efficient coding Bayesian ratio model.
(A) Bi-variate prior over log weight and log volume ratio, optimised to minimise errors in predicted log weight ratio. Red asterisk and dashed black line indicate an example stimulus condition and corresponding slice through the prior that are shown in part B. The solid red line is the identity line (i.e., equal density), and the dashed red line shows the orientation of the fitted prior (plotted over the stimulus range) as defined by its peak values. (B) Likelihood repulsion predicted by Wei and Stocker [29] for one stimulus condition with equal weight, unequal volume stimuli. Schematic of a median (unbiased/noise free) observer likelihood (red) and posterior (blue) for an example stimulus pair (red asterisk in A), given the 1D slice through prior (solid black line). Efficient coding of stimulus properties results in skewed likelihoods with a long tail away from the peak of the prior. The posterior is also skewed. When a symmetric loss function is chosen, e.g., the mean of the posterior (L2, blue dashed line), a bias away from the prior is predicted, i.e., the posterior estimate is shifted away from the prior peak, relative to the peak of the likelihood. Measurement noise (expected to be skewed in stimulus space) further increases the predicted repulsive bias [29]. (C-D) Biases in perceived log weight ratio. Contour lines show the prior; black dots show the stimulus pairs; arrows show the magnitude and direction of the bias for each pair, with SWI conditions in green; the solid red line shows equal density. (C) Empirical biases; (D) predicted biases.