ABSTRACT
This chapter examines the concept of conditional independence (CI) and provides an overview of both former and results on the description of CI structures. The idea to use graphs whose nodes correspond to random variables in order to describe CI structures had appeared in statistics earlier than J. Pearl and A. Paz suggested this approach in the context of computer science. The traditional graphical models, namely those ascribed to undirected graphs (UG) and directed acyclic graphs (DAG), can be interpreted as special cases of statistical models of a CI structure. UGs appeared in the 1970s in statistical physics as tools to describe relations among discrete random variables. J. Moussouris introduced several Markov properties relative to an UG for distributions with positive density and showed their equivalence with a factorization condition. In the 1980s, DAGs found their applications in the decision-making theory in connection with influence diagrams.
