Related papers: Chain graph models of multivariate regression type…
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, but also from cross-sectional or…
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.…
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…
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…
In this work we handle with categorical (ordinal) variables and we focus on the (in)dependence relationship under the marginal, conditional and context-specific perspective. If the first two are well known, the last one concerns…
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…
Classical linear regression is considered for a case when regression parameters depend on the external random environment. The last is described as a continuous time Markov chain with finite state space. Here the expected sojourn times in…
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…
We introduce multiple hidden Markov models (MHMMs) where an observed multivariate categorical time series depends on an unobservable multivariate Mar- kov chain. MHMMs provide an elegant framework for specifying various independence…
We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process…
Chain graphs combine directed and undirected graphs and their underlying mathematics combines properties of the two. This paper gives a simplified definition of chain graphs based on a hierarchical combination of Bayesian (directed) and…
A Markov network characterizes the conditional independence structure, or Markov property, among a set of random variables. Existing work focuses on specific families of distributions (e.g., exponential families) and/or certain structures…
We discuss two parameterizations of models for marginal independencies for discrete distributions which are representable by bi-directed graph models, under the global Markov property. Such models are useful data analytic tools especially…
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 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…
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…
Markov chains are a class of probabilistic models that have achieved widespread application in the quantitative sciences. This is in part due to their versatility, but is compounded by the ease with which they can be probed analytically.…
Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a…
Triplet Markov chains are general generative models for sequential data which take into account three kinds of random variables: (noisy) observations, their associated discrete labels and latent variables which aim at strengthening the…