Asymmetric separation for local independence graphs

2012/06/27 by Vanessa Didelez, Didelez, Vanessa
Computer Science · Biochemistry, Genetics and Molecular Biology · #Bayesian Modeling and Causal Inference #Gene Regulatory Network Analysis #Data Management and Algorithms

paper · doi:10.48550/arxiv.1206.6841

Abstract

Directed possibly cyclic graphs have been proposed by Didelez (2000) and Nodelmann et al. (2002) in order to represent the dynamic dependencies among stochastic processes. These dependencies are based on a generalization of Granger-causality to continuous time, first developed by Schweder (1970) for Markov processes, who called them local dependencies. They deserve special attention as they are asymmetric unlike stochastic (in)dependence. In this paper we focus on their graphical representation and develop a suitable, i.e. asymmetric notion of separation, called delta-separation. The properties of this graph separation as well as of local independence are investigated in detail within a framework of asymmetric (semi)graphoids allowing a deeper insight into what information can be read off these graphs.

Citations

• Investigating Causal Relations by Econometric Models and Cross-spectral Methods

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