Bernal S D_2010.pdf - University of Plymouth

3.3. DEFINITION AND MATHEMATlCACPORMULAnON
combining information from different image regions with a probabilistic prior favouring slow
and smooth velocities. In further support of this view, Kording and Wolpert (2004) concluded
that ihc central nervous system also employs a Bayesian inferential approach during sensorimo­
tor learning.
Probabilistic models arc currently widely used to successfully capture different aspects of brain
function, and provide a unifying perspective across a broad range of domains and levels of ab­
straction, They are not limited to modelling perception, and have been employed to explain
other cognitive functions such as psychological conditioning, semantic memory, and decision­
making (Chater el al. 2006). For example, a recent study employs a probabilistic inference
computational model, based on the neural representations in prefrontal cortex, to explain deci­
sion making during social interactions (Yoshidaet al. 2010).
3.3 Definition and mathemattcal formulation
In this section we define and formulate the mathematical tools used to develop the model in
this thesis, namely Bayesian networks and belief propagation. These provide a specific imple­
mentation of the theoretical principles described in Section 3.1, i.e. the Bayesian inference and
generative model framework. A body of experimental evidence highlighting the similarities be­
tween this approach and a set of functional, anatomical, physiological and biological properties
of the brain has been presented in Section 3.2.
This section first introduces basic probability theory concepts, and then describes what a Bayesian
network is and how belief propagation works, with the aid of a practical example. Subsequent
subsections describe two challenging aspects of belief propagation: combining infonnation
from multiple parents and dealing with loops in the network using approximate inference meth­
ods.
3.3.1 Probability theory
Before describing Bayesian networks in detail, and to facilitate understanding, this section in­
troduces some essential concepts and terminology from probability theory. Note capital letters
denote random variables, e.g. X, Y, while lower-case letters denote specific values of a random
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