One of the key factors for the acceptance of expert systems in real-world domains is the ability to explain their reasoning (Buchanan & Shortliffe, 1984; Henrion & Druzdzel, 1990). This paper describes the basic properties that characterise explanation methods and reviews the methods developed to date for explanation in Bayesian networks.

Explanation of reasoning is one of the most important abilities an expert system should provide in order to be widely accepted. In fact, since MYCIN, many expert systems have tried to include some explanation capability. This paper reviews the methods developed to date for explanation in heuristic expert systems.

Bayesian networks (BNs) and influence diagrams (IDs) are probabilistic graphical models that are widely used for building diagnosis- and decision-support expert systems. Explanation of both the model and the reasoning is important for debugging these models, alleviating users' reluctance to accept their advice, and using them as tutoring systems. This paper describes some explanation options for BNs and IDs that have been implemented in Elvira and how they have been used for building medical models and teaching probabilistic reasoning to pre- and postgraduate students.

A sum-product network (SPN) is a probabilistic model, based on a rooted acyclic directed graph, in which terminal nodes represent probability distributions and non-terminal nodes represent convex sums (weighted averages) and products of probability distributions. They are closely related to probabilistic graphical models, in particular to Bayesian networks with multiple context-specific independencies. Their main advantage is the possibility of building tractable models from data, i.e., models that can perform several inference tasks in time proportional to the number of edges in the graph. They are somewhat similar to neural networks and can address the same kinds of problems, such as image processing and natural language understanding. This paper offers a survey of SPNs, including their definition, the main algorithms for inference and learning from data, several applications, a brief review of software libraries, and a comparison with related models.