The material-weight illusion is a Bayes-optimal percept under competing density priors.

The material-weight illusion (MWI) is one example in a class of weight perception illusions that seem to defy principled explanation. In this illusion, when an observer lifts two objects of the same size and mass, but that appear to be made of different materials, the denser-looking (e.g., metal-look) object is perceived as lighter than the less-dense-looking (e.g., polystyrene-look) object. Like the size-weight illusion (SWI), this perceptual illusion occurs in the direction of predictions from an optimal Bayesian inference process, which predicts that the denser-looking object should be perceived as , not lighter. The presence of this class of illusions challenges the often-tacit assumption that Bayesian inference holds universal explanatory power to describe human perception across (nearly) all domains: If an entire class of perceptual illusions cannot be captured by the Bayesian framework, how could it be argued that human perception truly follows optimal inference? However, we recently showed that the SWI can be explained by an optimal hierarchical Bayesian causal inference process (Peters, Ma & Shams, 2016) in which the observer uses haptic information to arbitrate among competing hypotheses about objects' possible density relationship. Here we extend the model to demonstrate that it can readily explain the MWI as well. That hierarchical Bayesian inference can explain both illusions strongly suggests that even puzzling percepts arise from optimal inference processes.