Statistics and Data Science Seminar
Prof. Nanny Wermuth
Chalmers/Gothenburg University, Sweden
Consequences of research hypotheses captured by special types of independence graph
Abstract: A joint density of several variables may satisfy a possibly large set of independence statements, called its independence structure. Often this structure is fully representable by a graph that consists of nodes representing variables and of edges that couple node pairs. We consider joint densities of this type, generated by a stepwise process in which all variables and dependences of interest are included. Otherwise, there are no constraints on the type of variables or on the form of the distribution generated. For densities that then result after marginalising and conditioning, we derive what we name the summary graph. It is seen to capture precisely the independence structure implied by the generating process, it identifies dependences which remain undistorted due to direct or indirect confounding and it alerts to possibly severe distortions of these two types in other parametrizations. We use operators for matrix representations of graphs to derive matrix results and translate these into to special types of path.
Wednesday November 5, 2008 at 4:15 PM in SEO 612