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Knowledge about the statistical regularities of the world is essential for cognitive and sensorimotor function. In the domain of timing, prior statistics are crucial for optimal prediction, adaptation and planning. Where and how the nervous system encodes temporal statistics is, however, not known. Based on physiological and anatomical evidence for cerebellar learning, we develop a computational model that demonstrates how the cerebellum could learn prior distributions of time intervals and support Bayesian temporal estimation. The model shows that salient features observed in human Bayesian time interval estimates can be readily captured by learning in the cerebellar cortex and circuit level computations in the cerebellar deep nuclei. We test human behavior in two cerebellar timing tasks and find prior-dependent biases in timing that are consistent with the predictions of the cerebellar model.