Perceptual inference can be far more complex than simply reconstructing the optimal value of a parameter (orientation, speed, distance). Indeed, sensory inputs frequently result from a complex combination of numerous variables and noise sources. A visual scene, for example, is the result of a multi-level generative model that takes into account light sources, the probability of a given object being present, its shape, materials and their reflectance, etc. Bayesian networks make it possible to model this hierarchical propagation of constraints and to invert the model in order to reconstruct, from an image on the retina, the probability distribution of all parameters (Kersten, Mamassian & Yuille, 2004).
These hierarchical Bayesian models account for illusions such as the perception of the third dimension from illumination. The brain infers the presence of a light source, using thea priori that it probably comes from above, and this inferred information, in turn, is used to resolve ambiguity about the concave or convex shape of a half-sphere (Morgenstern, Murray & Harris, 2011).
Bayesian theory also clarifies how the brain integrates multiple sensory cues. In the presence of more or less noisy visual and tactile information, how do we decide, for example, on the size of an object? If the distributions are Gaussian, the theory makes precise predictions: perception should be a weighted average of the values suggested by each cue, while itsreliability (i.e. the inverse of variance) should be the sum of the reliabilities of each cue taken in isolation. Psychophysical research shows that human behavior conforms very precisely to these predictions (Ernst, 2007; Ernst & Banks, 2002). Bayesian theory also applies to the sequential integration of multiple cues (Petzschner & Glasauer, 2011).
