A graphical model or a probabilistic graphical model is a probabilistic model where the nodes of the graphs represent random variables, and the edges or the absence of them represent conditional independencies between variables. Graphical models thus provide a compact representation of joint probability distributions. The graduation seminar focuses on three groups of graphs: undirected graphs, directed acyclic graphs, and chain graphs. The rules for inferring conditional independencies from the graph are called Markov properties, specifically, we have pairwise Markov property, local Markov property, and global Markov property. Of these, the strongest is the global Markov property, as it provides the strictest criterion for inferring conditional independencies. The factorization property of density with respect to a given graph is also important, as it is directly related to conditional independence. For each group of graphs, an important result concerning the equivalence of the above mentioned properties is presented.
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