Related papers: Marginal log-linear parameters for graphical Marko…
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…
Marginal models involve restrictions on the conditional and marginal association structure of a set of categorical variables. They generalize log-linear models for contingency tables, which are the fundamental tools for modelling the…
Hidden variables are ubiquitous in practical data analysis, and therefore modeling marginal densities and doing inference with the resulting models is an important problem in statistics, machine learning, and causal inference. Recently, a…
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…
We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some…
Log-linear models are a classical tool for the analysis of contingency tables. In particular, the subclass of graphical log-linear models provides a general framework for modelling conditional independences. However, with the exception of…
Acyclic directed mixed graphs, also known as semi-Markov models represent the conditional independence structure induced on an observed margin by a DAG model with latent variables. In this paper we present the first method for fitting these…
The constraints arising from DAG models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs). Such graphs contain directed and bidirected arrows, and contain no directed cycles. DAGs with…
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…
This paper introduces a novel class of models for binary data, which we call log-mean linear models. The characterizing feature of these models is that they are specified by linear constraints on the log-mean linear parameter, defined as a…
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 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 study a class of conditional independence models for discrete data with the property that one or more log-linear interactions are defined within two different marginal distributions and then constrained to 0; all the conditional…
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…
This paper deals with the Bayesian analysis of graphical models of marginal independence for three way contingency tables. We use a marginal log-linear parametrization, under which the model is defined through suitable zero-constraints on…
We discuss a class of chain graph models for categorical variables defined by what we call a multivariate regression chain graph Markov property. First, the set of local independencies of these models is shown to be Markov equivalent to…
We provide results demonstrating the smoothness of some marginal log-linear parameterizations for distributions on multi-way contingency tables. First we give an analytical relationship between log-linear parameters defined within different…
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…
Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be…