On the differentiation theorem in metric groups
Convex cones in finite-dimensional real vector spaces
Asymptotic behaviour of empirical multiinformation
Attempts at axiomatic description of conditional independence
Contribution of František Matúš to the research on conditional independence
An overview is given of results achieved by F. Matúš on probabilistic conditional independence (CI). First, his axiomatic characterizations of stochastic functional dependence and unconditional independence are recalled. Then his elegant proof of discrete probabilistic representability of a matroid based on its linear representability over a finite field is recalled. It is explained that this result was a basis of his methodology for constructing a probabilistic representation of a given abstract...
Comparison of two methods for approximation of probability distributions with prescribed marginals
Let be a discrete multidimensional probability distribution over a finite set of variables which is only partially specified by the requirement that it has prescribed given marginals , where is a class of subsets of with . The paper deals with the problem of approximating on the basis of those given marginals. The divergence of an approximation from is measured by the relative entropy . Two methods for approximating are compared. One of them uses formerly introduced concept of...
Two operations of merging and splitting components in a chain graph
In this paper we study two operations of merging components in a chain graph, which appear to be elementary operations yielding an equivalent graph in the respective sense. At first, we recall basic results on the operation of feasible merging components, which is related to classic LWF (Lauritzen, Wermuth and Frydenberg) Markov equivalence of chain graphs. These results are used to get a graphical characterisation of factorisation equivalence of classic chain graphs. As another example of the use...
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