Visual perception can be understood as an inferential process that combines noisy sensory information with internalized knowledge drawn from previous experience. In statistical Bayesian terms, internal representations of the visual environment can be understood as posterior estimates obtained by weighting imperfect sensory information (a likelihood) by internalized biases (a prior). Given limited perceptual resources, it is advantageous for the visual system to capitalize on predictable regularities of the visual world, and internalize them in the form of priors. This dissertation presents novel findings in the domain of spatial vision and visual memory, as well as some new work on memory for the 3D orientation of objects. In all cases, an unprecedented signal-to-noise ratio, achieved by employing serial reproduction chains (a ``telephone game'' procedure) combined with non-parametric kernel density estimation techniques, reveals a number of stunning intricacies in the prior for the first time. Methodological implications, as well as implications for amending prior empirical findings and revisiting past theoretical explanations are discussed.