Reasoning with discrete factor graph

When working with probabilistic graphical models we usually have two options to build the model: either using a Bayesian network (BN) or a Markov random field (MRF). However, there exist one more graphical representation which is able to unify the properties of BN and MRF that is called Factor Graph. This paper describes conceptual methods in working with factor graph especially with discrete random variables, how to learn its parameter and how to perform inference for making a reasoning task with it. Here we use population coding principles to discretize continues values of messages transmitted within the factor graph to update the network's internal belief. We provide several illustrative examples to highlight important aspects when developing a model for factor graphs.