The neural representations of prior information about the state of the world are poorly understood. To investigate this issue, we examined brain-wide Neuropixels recordings and widefield calcium imaging collected by the International Brain Laboratory. Mice were trained to indicate the location of a visual grating stimulus, which appeared on the left or right with prior probability alternating between 0.2 and 0.8 in blocks of variable length. We found that mice estimate this prior probability and thereby improve their decision accuracy. Furthermore, we report that this subjective prior is encoded in at least 20% to 30% of brain regions which, remarkably, span all levels of processing, from early sensory areas (LGd, VISp) to motor regions (MOs, MOp, GRN) and high level cortical regions (ACCd, ORBvl). This widespread representation of the prior is consistent with a neural model of Bayesian inference involving loops between areas, as opposed to a model in which the prior is incorporated only in decision making areas. This study offers the first brain-wide perspective on prior encoding at cellular resolution, underscoring the importance of using large scale recordings on a single standardized task.

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