Footprints Sticking Out of the Sand. Part 2: Children's Bayesian Priors for Shape and Lighting Direction

The shading information in images that depict surfaces of 3-D objects cannot be perceived correctly unless the direction of the illuminating light source is known and, in the absence of this knowledge, perception in adults is consistent with a light-from-above Bayesian prior assumption. In order to investigate if children make use of a similar assumption, 171 children between the ages of 4.6 and 10.8 years were tested with 20 images containing shading information, where the shape depicted in each image could be perceived as either convex or concave. Each child's Bayesian prior probability that light comes from above was estimated, and (assuming that decision-noise is approximately the same in all children) regression analyses revealed a significant increase in this prior probability of 0.034–0.035 per year, and predict a neutral prior (0.5) at 1.6 years for naturalistic picture stimuli and 3.6 years for abstract symbol stimuli. Additionally, each child's prior probability for perceiving shapes as being convex/concave was estimated, and was found to be close to a neutral value of 0.5 for all ages. Together, these results indicate that children have a neutral prior for shape convexity, and that their prior probability for lighting direction gradually shifts towards an adult-like prior value as they grow older. Finally, the status of these one-dimensional priors is discussed in relation to marginal distributions of high-dimensional priors implicit in the statistical structure of the physical word.