Fig. 1.

Model evidence and posterior densities on the precision parameters of a general linear model. Upper left: the (exponential of the) free-energy bound on log-evidence as a function of prior mean and variance of the log-precision parameters of a general linear model. Lighter areas denote higher evidence. The dashed line represents the optimum prior mean that maximizes evidence. Upper right panel: this shows the model evidence as a function of prior variance at the optimum prior mean. Lower panel: this shows the posterior density on the first of two precision parameters. The solid line shows the (optimized) posterior, based upon the optimum priors, using Eq. (10) in the main text. The broken line represents the same quantity but under the full priors. The vertical doted line corresponds to the value (precision) of observation noise used to generate the data.