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Determining the approach of a moving object is a vital survival skill that depends on the brain combining information about lateral translation and motion-in-depth. Given the importance of sensing motion for obstacle avoidance, it is surprising that humans make errors, reporting an object will miss them when it is on a collision course with their head. Here we provide evidence that biases observed when participants estimate movement in depth result from the brain's use of a "prior" favoring slow velocity. We formulate a Bayesian model for computing 3D motion using independently estimated parameters for the shape of the visual system's slow velocity prior. We demonstrate the success of this model in accounting for human behavior in separate experiments that assess both sensitivity and bias in 3D motion estimation. Our results show that a surprising perceptual error in 3D motion perception reflects the importance of prior probabilities when estimating environmental properties. [ABSTRACT FROM AUTHOR]