Explanation, also known as beliefrevision, involves finding the most probable value (or discrete state) of one or more query variables given findings for other variables in the network. When all query nodes are ancestors ofnodes with findings, this is referred to as identifying the most probable explanation (MPE). For example, in Figure 3, after observing the occurrence of a fishkill (K), one might want to know the most likely coincident level of algal toxins (T) or hypoxia (H). This amounts to finding the MPE. The problem offinding the MPE is a special case of probabilistic inference and is also NP-hard.

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