BAYES AND THE SIMPLICITY PRINCIPLE IN PERCEPTION 11
Two governing principles of perceptual inference, the Like lihood principle and the Simplicity principle, have been much discussed by perceptual theorist s, and often placed in opposition. Recently, Chater (1996) has argued that the two principles a r actually consistent in that their decisions tend to agree asymptotically. This article seeks to relate in a more mathematically direct way what is arguably the most plausible version of a like lihood theory, Bayesian inference, with a recently-proposed generalized formal minimum princ iple (the maximum-depth rule of Minimal Model theory). Assuming qualitative information o n the part of the observer, and equal prior probabilities among among all competing hypoth eses, maximizing the Bayesian posterior probability turns out to be mathematically equiv alent to choosing the maximumdepth interpretation from a hierarchical space of possible scene interpretations. That is, the maximum-depth rule is analytically equivalent to Bayes wit h a particular choice of priors. Thus this version of the Simplicity principle, as well as “full-b own Bayes,” each constitute distinct points in a well-defined continuum of possible perceptual de cision rules. In a very literal mathematical sense, the observer’s position in this continuum— and, consequently, the perceptual decision rule it employs—reflect the nature of its tacit assu mptions about the environment.