puzzle, giving rise to a variety of theories about its neural basis. The prevailing physiological models of motion perception have generally been based on a processing hierarchy in which the lower-order receptive field properties of motion sensitive neurons in V1 are used to progressively construct the more complex responses of higher-order cortical regions such as those observed in areas MT and MST in the non-human primate brain and MT+ in humans, the culmination of this process being the motion perceived [16–22]. Although this approach has been amended with two-stage [23] or three-stage [24] processing schemes, as well as by the addition of ‘‘component cells,’’ ‘‘pattern cells,’’ and cascade models that could explain further details of motion perception [25,26], this idea remains a popular conception of how motion percepts are generated. In addition to physiological models of visual motion, a number of other models have been proposed. Of these, algorithmic strategies for feature-detection [13,14,27–29], spatiotemporal energy models [30–34], and Bayesian approaches have received the most attention. Although each of these models can explain some important aspects of motion perception, none explains the extraordinary range of anomalous motion percepts experienced by observers, including the psychophysical results we report here. Consider, for instance, whether application of Bayesian decision theory to the simulation data would have predicted the observed psychophysical functions in the Results. The problem we addressed can be easily formulated in Bayesian terms. Since the goal of a Bayesian model is to estimate the most probable 3-D source based on the available 2-D evidence, the variables pertinent to the current study are the 3-D object speed, 2-D image speed, and 2-D image distance (recall that since the reference and test stimuli always moved horizontally from left-to-right, perceived direction does not need to be considered). These parameters can be exp- ressed in Bayesian terms as, P(3D speedj2D speed, 2D distance) Perceiving Motion Empirically P(3D speed).P(2D speed, 2D distancej3D speed) ~ where P is P(2D speed, 2D distance) probability. In this formulation, the first term on the right side of the equation, P(3D speed), is the prior probability distribution, which describes the experience of human observers with 3-D speeds. Because this distribution in the simulation was uniform, the shape of the prior is also uniform. The second term on the right side of the equation, P(2D speed, 2D distance | 3D speed), is the likelihood function, which describes the probability that a given 3- D speed will have generated any specific 2-D image speed and distance. The product of the prior and relevant likelihood function divided by a normalization constant, P(2D speed, 2D distance), generates the posterior probability distribution, P(3D speed | 2D speed, 2D distance). The posterior distribution is therefore a subset of the prior, indicating the relative probabilities of possible 3-D object speeds that could have produced a specific 2-D image sequence in question. Since in a Bayesian formulation motion percepts correspond to a particular value in the posterior distribution, a basis for choosing this value is needed. Typically, this criterion is the presumed biological usefulness of the value; under the assumption that this would be the most frequently occurring source in past experience, an index such as the mean, median, or mode of the posterior distribution is used to generate the value that determines the percept. To predict the psychophysical observations reported in the Results in Bayesian terms, we calculated posterior probability distributions for stimuli traversing 1u–7u of projected distance at 6.5u/s (Figure 8; posterior distributions for each of the image speeds tested in the psychophysical studies were similarly derived). As indicated in Figure 7B, the psychophysical data showed that, for stimuli traversing projected distances of 1u–7u at 6.5u/s, the perceived speed decreased progressively as the projected distance increased. In a Bayesian formulation, however, the mean of each posterior probability distribution in Figure 8 predicts that Figure 8. Bayesian posterior probability distributions for stimuli traversing projected distances of 1u–7u at 6.5u/s. For each projected distance from 1u–7u, the probability of 3-D speeds that can give rise to an image speed of 6.5u/s are shown. Calculating the mean, median, or mode of each distribution results in the predicted percept for the specific projected distance. Similar distributions for the other image speeds tested (2.6u/s, 3.9u/s, 7.8u/s, and 10.4u/s) were generated, but are not shown. doi:10.1371/journal.pone.0006771.g008 PLoS ONE | www.plosone.org 9 August 2009 | Volume 4 | Issue 8 | e6771