Neural circuits encode prior knowledge of temporal statistics.

The brain must infer the state of the external world despite the inherent uncertainty of its sensory inputs and internal processes. Under conditions of heightened uncertainty, it increasingly relies on prior knowledge, derived from accumulated experience with the regularities and statistical structures of the environment. This principle has been formalized by Bayesian inference theories, which are supported by substantial evidence from both behavioral and neuroscience studies. However, direct evidence for the existence of prior knowledge in the brain, and for the encoding of environmental statistics by neural circuits, remains limited. Here we show that cerebellar circuits learn the prior probability distribution of temporal variables during eyeblink conditioning in mice and encode these representations in Purkinje cell simple and complex spike signaling. We further demonstrate that Purkinje cells are involved in eliciting predictive motor behaviors, such as the conditioned eyeblink response, that also reflect the statistics of the experimentally imposed prior distribution of the stimulus. Computational modeling of these results indicates the juxtaposition of counteracting long-term plasticity mechanisms by which cerebellar Purkinje cells could acquire prior knowledge that is shaped by the statistics of different probability distributions. Our results suggest that the cerebellar circuitry may be uniquely poised to learn the probability of events in the world and internalize these as prior knowledge. These findings advance understanding of how neural computations could implement Bayesian inference.