  The 'free energy principle' (FEP) has been suggested to provide a unified
theory of the brain, integrating data and theory relating to action,
perception, and learning. The theory and implementation of the FEP combines
insights from Helmholtzian 'perception as inference', machine learning theory,
and statistical thermodynamics. Here, we provide a detailed mathematical
evaluation of a suggested biologically plausible implementation of the FEP that
has been widely used to develop the theory. Our objectives are (i) to describe
within a single article the mathematical structure of this implementation of
the FEP; (ii) provide a simple but complete agent-based model utilising the
FEP; (iii) disclose the assumption structure of this implementation of the FEP
to help elucidate its significance for the brain sciences.
