Causality, Conditional Independence, and Graphical Separation in Settable Systems

Independence and Conditional Independence in Causal Systems

This paper studies the interrelations between independence or conditional independence and causal relations, defined in terms of functional dependence, that hold among variables of interest within the settable system framework of White and Chalak. We provide formal conditions ensuring the validity of Reichenbach’s principle of common cause and introduce a new conditional counterpart, the condit...

Logical and Algorithmic Properties of Conditional Independence and Graphical Models

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Conditional Independence in Directed Cyclic Graphical Models for Feedback

Graphical and Algebraic Representatives of Conditional Independence Models

The topic of this chapter is conditional independence models. We review mathematical objects that are used to generate conditional independence models in the area of probabilistic reasoning. More specifically, we mention undirected graphs, acyclic directed graphs, chain graphs, and an alternative algebraic approach that uses certain integer-valued vectors, named imsets. We compare the expressiv...

Marginal conditional independence models with application to graphical modeling

Conditional independence models are defined by a set of conditional independence restrictions and play an important role in many statistical applications, especially, but not only, graphical modeling. In this paper we identify a subclass of these models which are hierarchical marginal log-linear, as defined by Bergsma and Rudas (2002a). Such models are smooth, which implies the applicability of...