Figure 1.

(A) An informative central prior (green area) leads to a bias of the sensory measurements (likelihoods, red curves) toward the peak of the prior. The posterior estimate (gray area) has higher precision than the prior or the likelihood but is systematically shifted toward the center of the range of stimulus magnitudes, which generates the characteristic central-tendency bias. As an observed behavioral consequence, the central-tendency bias is expressed by a negative trend of estimation errors measured as a function of stimulus magnitudes, which turns the overestimation of small stimulus magnitudes into an underestimation of large stimulus magnitudes. (B) An uninformative (flat) prior (green area) does not generate a central-tendency bias. The posterior estimates (gray areas) have the same precision as the sensory judgments (likelihoods, red curves) and are not shifted from the likelihoods. As a consequence, the observed average measurement error is unbiased with no systematic over- or underestimation of stimulus magnitudes within the test range. (C) A weakly informative uniform prior with truncated support, which assigns equal probabilities to the stimulus magnitudes within a certain range, leads to the prediction of an attenuated central-tendency bias. The posterior estimates (gray areas) have higher precision than the likelihoods (red curves) and are truncated at the boundaries of the prior.