Mapping eQTL Networks with Mixed Graphical Markov Models

Mapping eQTL networks with mixed graphical Markov models.

Expression quantitative trait loci (eQTL) mapping constitutes a challenging problem due to, among other reasons, the high-dimensional multivariate nature of gene-expression traits. Next to the expression heterogeneity produced by confounding factors and other sources of unwanted variation, indirect effects spread throughout genes as a result of genetic, molecular, and environmental perturbation...

Graphical Markov Models with Mixed Graphs in R

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 of edges) that are important because they capture the modified independence structure after marginalisation over, and conditioning on, nodes of directed acyclic graphs. We provide functions to verify w...

Introduction to Graphical Models, Hidden Markov Models and Bayesian Networks

Graphical Markov Models

Graphical Markov models are multivariate statistical models which are currently under vigorous development and which combine two simple but most powerful notions, generating processes in single and joint response variables and conditional independences captured by graphs. The development of graphical Markov started with work by Wermuth (1976, 1980) and Darroch, Lauritzen and Speed (1980) which ...

Graphical Markov Models: Overview

We describe how graphical Markov models emerged in the last 40 years, based on three essential concepts that had been developed independently more than a century ago. Sequences of joint or single regressions and their regression graphs are singled out as being the subclass that is best suited for analyzing longitudinal data and for tracing developmental pathways, both in observational and in in...