Description of structures of stochastic conditional independence by means of faces and imsets .3. Examples of use and appendices
This part contains several examples that illustrate the implementation of the facial deductive mechanism and show how to transform information about conditional independence structure given in the form of dependency models, Bayesian or Markov networks into imsets. Another example indicates that the facial deductive mechanism is indeed more powerful than the semigraphoid one. A simple method of proving the probabilistic soundness of an inference rule is presented. Two appendices contain some supplementary results about the structural ordering of imsets. The advantages and disadvantages of and prospects For the presented approach are discussed in the Conclusions.
conditional independence imset markov network bayesian network facial implication portrait