On Probabilistic Independence Models and Graphs
The main purpose of this talk is to explore the relationship between the set of conditional independence statements induced by a probability distribution and the set of separations induced by graphs as studied in graphical models. I introduce the concepts of Markov property and faithfulness, and provide conditions under which a given probability distribution is Markov or faithful to a graph. I use these results to provide implications on independence of exchangeable random vectors and networks. I also discuss possible probability theoretic problems related to the results.