Prediction, Postdiction, and Perceptual Length Contraction: A Bayesian Low-Speed Prior Captures the Cutaneous Rabbit and Related Illusions

Daniel Goldreich, Jonathan Tong

Illusions provide a window into the brain's perceptual strategies. In certain illusions, an ostensibly task-irrelevant variable influences perception. For example, in touch as in audition and vision, the perceived distance between successive punctate stimuli reflects not only the actual distance but curiously the inter-stimulus time. Stimuli presented at different positions in rapid succession are drawn perceptually toward one another. This effect manifests in several illusions, among them the startling cutaneous rabbit, in which taps delivered to as few as two skin positions appear to hop progressively from one position to the next, landing in the process on intervening areas that were never stimulated. Here we provide an accessible step-by-step exposition of a Bayesian perceptual model that replicates the rabbit and related illusions. The Bayesian observer optimally joins uncertain estimates of spatial location with the expectation that stimuli tend to move slowly. We speculate that this expectation - a Bayesian prior - represents the statistics of naturally occurring stimuli, learned by humans through sensory experience. In its simplest form, the model contains a single free parameter, tau: a time constant for space perception. We show that the Bayesian observer incorporates both pre- and post-dictive inference. Directed spatial attention affects the prediction-postdiction balance, shifting the model's percept toward the attended location, as observed experimentally in humans. Applying the model to the perception of multi-tap sequences, we show that the low-speed prior fits perception better than an alternative, low-acceleration prior. We discuss the applicability of our model to related tactile, visual, and auditory illusions. To facilitate future model-driven experimental studies, we present a convenient freeware computer program that implements the Bayesian observer; we invite investigators to use this program to create their own testable predictions.