Related papers: An Alternative Markov Property for Chain Graphs

Acyclic directed mixed graphs (ADMGs) are graphs that contain directed ($\rightarrow$) and bidirected ($\leftrightarrow$) edges, subject to the constraint that there are no cycles of directed edges. Such graphs may be used to represent the…

Chain graphs (CG) use undirected and directed edges to represent both structural and associative dependences. Like acyclic directed graphs (ADGs), the CG associated with a statistical Markov model may not be unique, so CGs fall into Markov…

We present a new family of models that is based on graphs that may have undirected, directed and bidirected edges. We name these new models marginal AMP (MAMP) chain graphs because each of them is Markov equivalent to some AMP chain graph…

Depending on the interpretation of the type of edges, a chain graph can represent different relations between variables and thereby independence models. Three interpretations, known by the acronyms LWF, MVR, and AMP, are prevalent.…

We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that…

Several types of graphs with different conditional independence interpretations --- also known as Markov properties --- have been proposed and used in graphical models. In this paper we unify these Markov properties by introducing a class…

The AMP Markov property is a recently proposed alternative Markov property for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced LWF Markov…

We introduce a new class of graphical models that generalizes Lauritzen-Wermuth-Frydenberg chain graphs by relaxing the semi-directed acyclity constraint so that only directed cycles are forbidden. Moreover, up to two edges are allowed…

We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such…

We extend Andersson-Madigan-Perlman chain graphs by (i) relaxing the semidirected acyclity constraint so that only directed cycles are forbidden, and (ii) allowing up to two edges between any pair of nodes. We introduce global, and ordered…

Conditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the d-separation criterion), and the local…

Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional…

Global Markov properties in mixed graphs are usually formulated in terms of the path-oriented m-separation or by use of augmented graphs (similar to moral graphs in the case of directed acyclic graphs). We provide an alternative…

Current approaches for modeling discrete-valued outcomes associated with spatially-dependent areal units incur computational and theoretical challenges, especially in the Bayesian setting when full posterior inference is desired. As an…

The statistical literature discusses different types of Markov properties for chain graphs that lead to four possible classes of chain graph Markov models. The different models are rather well understood when the observations are continuous…

This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov…

Global variational approximation methods in graphical models allow efficient approximate inference of complex posterior distributions by using a simpler model. The choice of the approximating model determines a tradeoff between the…

Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing.…

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series…

Maximal ancestral graphs (MAGs) are used to encode conditional independence relations in DAG models with hidden variables. Different MAGs may represent the same set of conditional independences and are called Markov equivalent. This paper…