This paper introduces a class of graphical independence models that is closed under
marginalization and conditioning but that contains all DAG independence models. This class …

Chain graphs are a natural generalization of directed acyclic graphs and undirected graphs.
However, the apparent simplicity of chain graphs belies the subtlety of the conditional …

We consider a variety of ways in which probabilistic and causal models can be represented
in graphical form. By adding nodes to our graphs to represent parameters, decision, etc., we …

From the Publisher: The concept of modelling using graph theory has its origin in several
scientific areas, notably statistics, physics, genetics, and engineering. The use of graphical …

A class of graphs is introduced which is closed under marginalizing and conditioning. It is
shown that these operations can be executed by performing in arbitrary order a sequence of …

The topic of this survey are structures of stochastic conditional independence. Two basic
questions are dealt with: the problem of characterization of conditional independence …

Abstract Two or more Bayesian Networks are Markov equivalent when their corresponding
acyclic digraphs encode the same set of conditional independence (≡ CI) restrictions …

Technological advances have led to new and automated data collection methods. Datasets
once at a premium are often plentiful nowadays and sometimes indeed massive. A new …

It has been shown in Richardson and Spirtes (2000) that if an ancestral graph is not
maximal, then there exists at least one pair of vertices {o:,, B} that are not adjacent, for which …

Computation is, nowadays, one of the most influential aspects in most fields of scientific
research. Until the moment in which computation has obtained such relevance, the problem …