Bernal S D_2010.pdf - University of Plymouth

XI. THEBAYESIANBRAINHYPfmBSIS
posterior probability of the causes given the inputs (mapping from sensations to causes). This
can be written as:
where P{C\I) represents the posterior probabihty of the causes C given the input /, for example
the probability over the different physical causes given a particular retinal image; P{I\C) rep­
resents the likelihood of the input / given the causes C, for example the probability of a given
retinal image having been generated by one or another of the potential different physical causes;
P(C) represents the prior probability of the causes C, for example the different physical slates
of the world; and P{!] simply represents a normalization factor
3.1.3 Free-energy principle
The free-energy principle proposed by Prislon (Friston and Kiebel 2009, Friston lOOfi, Friston
et al. 2006, Friston 2010) conceptualizes the brain as an adaptive system which tries to resist
a natural tendency to disorder, or entropy. Entropy can also be understood as a measure of
unccnainiy or surprise, thus informally, the system needs to avoid surprises to ensure its state
remains wiihin physiological bounds. One of the main characteristics of biological systems is
ihal they maintain their internal stales within operational bounds, even with constantly changing
environments.
However, how can a system know if its sensations are surprising? The free energy principle
provides a framework to do this as the free energy of a system is an upper bound on surprise.
Thus by minimizing free energy, the system is implicitly minimizing surprise. Importantly, free
energy can be evaluated because it depends on two probability densities which are available to
the system: the recognition density and the conditional or posterior density.
The recognition density, P(i?|^). provides a probabilistic representation of the causes. iJ, of a
particular stimulus, given a set of internal slates, /i. In the brain these internal states hypolheli-
cally correspond to neuronal activity and synaptic weights. The conditional density, P{s. i?|m).
provides the joint probabilistic representation of causes, i?, and sensory signals, s. It is based
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