Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies,â€¦ (More)

In this paper we study classes of graphs with three types of edges that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variablesâ€¦ (More)

In this thesis we describe subclasses of a class of graphs with three types of edges, called loopless mixed graphs (LMGs). The class of LMGs contains almost all known classes of graphs used in theâ€¦ (More)

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 independenceâ€¦ (More)

Abstract: We introduce the beta model for random hypergraphs in order to represent the occurrence of multi-way interactions among agents in a social network. This model builds upon and generalizesâ€¦ (More)

In this paper we provide a short tutorial illustrating the new functions in the package ggm that deal with ancestral, summary and ribbonless graphs. These are mixed graphs (containing three types ofâ€¦ (More)

Several types of graphs with different conditional independence interpretations â€” also known as Markov properties â€” have been proposed and used in graphical models. In this paper we unify theseâ€¦ (More)

A main question in graphical models and causal inference is whether, given a probability distribution P (which is usually an underlying distribution of data), there is a graph (or graphs) to which Pâ€¦ (More)

Joint degree vectors give the number of edges between vertices of degree i and degree j for 1 6 i 6 j 6 n âˆ’ 1 in an n-vertex graph. We find lower and upper bounds for the maximum number of nonzeroâ€¦ (More)