Introduction to Graphical Modelling

By Graham J. Wills. Technometrics, 2002

497 citations recorded by the source corpus.

Subfields: Industrial and Manufacturing Engineering

View Paper: https://www.semanticscholar.org/paper/a6217ddda1b81a244ea4a26520e16bf38aa04c7d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Industrial and Manufacturing Engineering

1. Thomas S. Richardson
2. Ji Zhu
3. R. Greiner
4. Lingzhou Xue
5. Ming Yuan
6. D. R. Cox
7. José M. F. Moura
8. Zudi Lu

Citations in the corpus

• High Dimensional Semiparametric Gaussian Copula Graphical Models. (2012, methodology): “sume that Y has a multivariate Gaussian distribution with inverse covariance matrix (also called the concentration matrix or the precision matrix) , then test the sparsity pattern of (Dempster, 1972; Edwards, 1995). Drton and Perlman (2007, 2008) have developed this method in detail. A drawback is t”
• Graph Signal Processing: Overview, Challenges, and Applications (2017, background): “Acyclic graphs [31], [32] represent Bayesian networks, and undirected graphs represent Markov random fields [33], [34], [35].”
• Model selection and estimation in the Gaussian graphical model (2007, background): “It has long been recognized that this procedure does not correctly take account of the multiple comparisons involved (Edwards, 2000).”
• Panning for Gold: Model-free Knockoffs for High-dimensional Controlled Variable Selection (2016, background): “For example, the textbook Edwards (2000) describes these properties on page 8 as holding “under quite general conditions” and then assumes them for the rest of the book.”
• Premature age-related comorbidities among HIV-infected persons compared with the general population. (2011, unknown): “dk/) [22].”
• Joint response graphs and separation induced by triangular systems (2004, methodology): “For different perspectives on the statistical models that are associated with such independence graphs, see Cox and Wermuth (1996), Edwards (2000), Green et al. (2003), Lauritzen (1996) and Whittaker (1990).”
• Testing conditional independence for continuous random variables (2004, unknown): “Edwards (2000) based his analyses on the partial correlation coefficient (1) assuming linear regression functions g and h.”
• Partial Correlation Estimation by Joint Sparse Regression Models (2008, methodology): “It is shown that space performs well in both nonzero partial correlation selection and the identification of hub variables, and also outperforms two existing methods.”
• Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm (2005, background): “A proof can be found in Fisher (1924); see also Anderson (1984).”
• Discrete Signal Processing on Graphs (2012, background): “For example, directed (acyclic) graphs [11], [12] represent Bayesian networks where each random variable is independent of others given the variables defined on its parent nodes.”
• Alternative Markov Properties for Chain Graphs (2001, methodology): “By normality, this is equivalent to the following condition: u, v 2 ô, u, v not adjacent in Gô ) (Ëÿ1ô )uv 0, (23) that is, Ëô satis®es the covariance selection model (Dempster, 1972; Lauritzen, 1996, prop.”
• Learning Bayesian networks from data: An information-theory based approach (2002, methodology): “Appendix C. Introduction to BN PowerSoft Package There are several commercial systems and research prototypes for learning Bayesian networks from data, including TETRAD II [44], Bayesian Knowledge Discoverer [42], CoCo [4], BUGS [54], BIFROST [32] and MIM [21].”
• Stability Approach to Regularization Selection (StARS) for High Dimensional Graphical Models (2010, background): “Gaussian graphical models [4, 23, 5, 9] are by far the most popular approach for learning high dimensional undirected graph structures.”
• Sequences of regressions and their independences (2011, methodology): “An extension to graphs including a concentration graph had already been proposed for directed acyclic graphs by Kiiveri et al. (1984). By this type of extension, the global Markov property of the graph remains unchanged.”
• Multivariate Statistical Analysis (2011, background): “This can be recognized to be one special type of a graphical Markov model; see Cox and Wermuth (1996), Edwards (2000), Lauritzen (1996), Whittaker (1990).”
• Bayesian group factor analysis with structured sparsity (2016, methodology): “The partial correlation between gene j1 and j2, representing the correlation between the two features conditioned on the remaining features, is then calculated by normalizing each entry in the precision matrix (Edwards, 2000; Schäfer and Strimmer, 2005):”