Figure 1.

This schematic illustrates the importance of precision when forming posterior beliefs and expectations. The graphs show Gaussian probability distributions that represent prior beliefs, posterior beliefs, and the likelihood of some data or sensory evidence as functions of some hidden (unknown) parameter. The dotted line corresponds to the posterior expectation, while the width of the distributions corresponds to their dispersion or variance. Precision is the inverse of this dispersion and can have a profound effect on posterior beliefs. Put simply, the posterior belief is biased toward the prior or sensory evidence in proportion to their relative precision. This means that the posterior expectation can be biased toward sensory evidence by either increasing sensory precision – or failing to attenuate it – or by decreasing prior precision.