Related papers: Graphical Markov models for infinitely many variab…
Probabilistic independence can dramatically simplify the task of eliciting, representing, and computing with probabilities in large domains. A key technique in achieving these benefits is the idea of graphical modeling. We survey existing…
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.…
In this work, we consider an extension of graphical models to random graphs, trees, and other objects. To do this, many fundamental concepts for multivariate random variables (e.g., marginal variables, Gibbs distribution, Markov properties)…
The fundamental concepts underlying in Markov networks are the conditional independence and the set of rules called Markov properties that translates conditional independence constraints into graphs. In this article we introduce the concept…
Graphical models are used to describe the conditional independence relations in multivariate data. They have been used for a variety of problems, including log-linear models (Liu and Massam, 2006), network analysis (Holland and Leinhardt,…
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…
Graphical models express conditional independence relationships among variables. Although methods for vector-valued data are well established, functional data graphical models remain underdeveloped. We introduce a notion of conditional…
Symmetric independence relations are often studied using graphical representations. Ancestral graphs or acyclic directed mixed graphs with $m$-separation provide classes of symmetric graphical independence models that are closed under…
We introduce a novel class of graphical models, termed profile graphical models, that represent, within a single graph, how an external factor influences the dependence structure of a multivariate set of variables. This class is quite…
In this work, we propose a global model selection criterion to estimate the graph of conditional dependencies of a random vector based on a finite sample. By global criterion, we mean optimizing a function over the entire set of possible…
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…
Markov models lie at the interface between statistical independence in a probability distribution and graph separation properties. We review model selection and estimation in directed and undirected Markov models with Gaussian…
Conditional independence and graphical models are well studied for probability distributions on product spaces. We propose a new notion of conditional independence for any measure $\Lambda$ on the punctured Euclidean space $\mathbb…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of…
With a sequence of regressions, one may generate joint probability distributions. One starts with a joint, marginal distribution of context variables having possibly a concentration graph structure and continues with an ordered sequence of…
We derive an explicit link between Gaussian Markov random fields on metric graphs and graphical models, and in particular show that a Markov random field restricted to the vertices of the graph is, under mild regularity conditions, a…
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such…
Classical graphical modeling of multivariate random vectors uses graphs to encode conditional independence. In graphical modeling of multivariate stochastic processes, graphs may encode so-called local independence analogously. If some…
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…