Abstract :Statistical regularities in the environment create prior beliefs that we rely on to optimize our behavior when sensory information is uncertain. Bayesian theory formalizes how prior beliefs can be leveraged and has had a major impact on models of perception, sensorimotor function, and cognition. Little is known, however, about how prior knowledge is acquired and utilized by neural circuits to carry out computations that optimize our motor and cognitive behaviors. I will first talk about previous work in monkeys that perform timing behaviors consistent with Bayesian inference. We found that neurons in the medial frontal cortex began modulating at the earliest probable interval in the prior distribution. Recently, we have traced the potential origins of this phenomenon to cerebellar circuits, which provide disynaptic input to the medial frontal cortex. We looked at single unit activity of cerebellar Purkinje cells for different prior distributions, including when mice switched from one prior to another. Furthermore, we discovered a unique complex spike signal in Purkinje cells that indicates the onset of the prior. We used optogenetics and chronic lesions to establish cerebellar involvement in prior-related predictive behavior. To understand potential mechanisms, we propose a biophysical model that could explain how Purkinje cells acquire and encode temporal prior knowledge for downstream processing by areas like the medial frontal cortex. In the final part of the talk, I will make a case for how neural populations could encode prior knowledge as neural manifolds and briefly discuss a new manifold learning technique that could help test Bayesian hypotheses in neural populations, alongside a spate of other neuroscientific applications.