The tau effect is a spatial perceptual illusion that arises when observers judge the distance between consecutive stimuli in a stimulus sequence.
[9] One limitation of this theory, pointed out by Goldreich (2007),[10] is that it does not explain why even two stimuli pressed in rapid succession against the skin are perceived as closer together the shorter the temporal interval between them is.
In the absence of a third stimulus that creates a second spatial and temporal interval, the constant velocity hypothesis can have no bearing on this two-stimulus situation.
The Bayesian model reaches an optimal probabilistic inference by combining uncertain spatial and temporal sensory information with a prior expectation for low-speeds.
Unlike the constant velocity hypothesis, the Bayesian model replicates the underestimation in perceived distance that occurs even when only two stimuli are presented in rapid succession.
For the case of two taps to the skin, the Bayesian model [11] perceives the length between taps, l*, to be a function of the actual length, l, and the elapsed time, t: l* = l/1 + 2(τ/t)2 The parameter tau (τ) is proportional to the observer's spatial uncertainty (specifically, it is the spatial standard deviation divided by the low-speed prior standard deviation).
He noted that, when stimuli move rapidly across space, "perception strikingly shrinks the intervening distance, and expands the elapsed time, between consecutive events".