Title: Using vine copulas to estimate the structure of directed acyclical graphs
Authors: Eugen Pircalabelu - Université catholique de Louvain (Belgium) [presenting]
Abstract: A new method of estimating and selecting a Bayesian network for continuous data is presented with the goal of stepping outside the class of multivariate normal distributions which are generally used due to their attractive properties. The method combines directed acyclic graphs and their associated probability models with copula C/D vines in order to construct `copula based DAGs' which allow more flexibility in modeling joint distributions of pairs of nodes in the network. We exploit connections and similarities that exist between these two statistical techniques with the explicit purpose of estimating a directed graphical model, a network, for continuous data that are not necessarily normally distributed. The approach uses a score based learning scheme, where one modifies an initial graph based on improvements in the score, until a local maximum score is reached. A new information criterion is proposed and studied for graph selection tailored to the joint modeling of data based on graphs and copulas. Examples and simulation studies show the flexibility and properties of the method.