Semidefinite tests for latent causal structures

In spite of the primal importance of discovering causal relations in science, the statistical analysis of empirical data has historically shied away from causality . Only releatively recently has a rigorous theory of causality emerged (see, for instance, [ 1, 2 ]), showing that empirical data indeed can contain information about causation rather than mere correlation. Since then, causal inference has quickly become influential. Examples range from applications to the inference of genetic [ 3] and social networks [ 4], to a better understanding of the role of causality within quantum physics [ 5-13]. T o formalize causal mechanisms it has become popular to use directed acyclic graphs (DAGs) where nodes denote random variables and directed edges (arrows) account for their causal relations. Central problems within this context include inferenceor model selection: 'Given samples from a number of observable variables, which DAG should we associate with them?', as well as hypothesis testing: 'Can the observed data be explained in terms of an assumed DAG?' Here, we concentrate on the latter problem and propose a novel solution based on the covariances that a given causal structure gives rise to.