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 …

We describe how graphical Markov models started to emerge in the last 40 years, based on
three essential concepts that had been developed independently more than a century ago …

Ordered sequences of univariate or multivariate regressions provide statistical models for
analysing data from randomized, possibly sequential interventions, from cohort or multi …

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 …

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 …

A set of independence statements may define the independence structure of interest in a
family of joint probability distributions. This structure is often captured by a graph that …

In this paper, we define and study the concept of traceable regressions and apply it to some
examples. Traceable regressions are sequences of conditional distributions in joint or single …

We introduce and study a subclass of joint Bernoulli distributions which has the palindromic
property. For such distributions the vector of joint probabilities is unchanged when the order …

Graphical Markov models combine conditional independence constraints with graphical
representations of stepwise data generating processes. The models started to be formulated …

To observe and understand relations among several features of individuals or objects is one
of the central tasks in many substantive fields of research, including the medical, social …