  Artificial Intelligence (AI), and in particular, the explainability thereof,
has gained phenomenal attention over the last few years. Whilst we usually do
not question the decision-making process of these systems in situations where
only the outcome is of interest, we do however pay close attention when these
systems are applied in areas where the decisions directly influence the lives
of humans. It is especially noisy and uncertain observations close to the
decision boundary which results in predictions which cannot necessarily be
explained that may foster mistrust among end-users. This drew attention to AI
methods for which the outcomes can be explained. Bayesian networks are
probabilistic graphical models that can be used as a tool to manage
uncertainty. The probabilistic framework of a Bayesian network allows for
explainability in the model, reasoning and evidence. The use of these methods
is mostly ad hoc and not as well organised as explainability methods in the
wider AI research field. As such, we introduce a taxonomy of explainability in
Bayesian networks. We extend the existing categorisation of explainability in
the model, reasoning or evidence to include explanation of decisions. The
explanations obtained from the explainability methods are illustrated by means
of a simple medical diagnostic scenario. The taxonomy introduced in this paper
has the potential not only to encourage end-users to efficiently communicate
outcomes obtained, but also support their understanding of how and, more
importantly, why certain predictions were made.
