Introduction to Graphical Modelling. Graphic modelling is a form of multivariate analysis that uses graphs to represent models. These graphs display the structure of dependencies, both associational and causal, between the variables in the model. This textbook provides an introduction to graphical modelling with emphasis on applications and practicalities rather than on a formal development. It is based on the popular software package for graphical modelling, MIM, a freeware version of which can be downloaded from the Internet. Following an introductory chapter which sets the scene and describes some of the basic ideas of graphical modelling, subsequent chapters describe particular families of models, including log-linear models, Gaussian models, and models for mixed discrete and continuous variables. Further chapters cover hypothesis testing and model selection. Chapters 7 and 8 are new to the second edition. Chapter 7 describes the use of directed graphs, chain graphs, and other graphs. Chapter 8 summarizes some recent work on causal inference, relevant when graphical models are given a causal interpretation. This book will provide a useful introduction to this topic for students and researchers.

References in zbMATH (referenced in 121 articles , 2 standard articles )

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  1. Fan, Jianqing; Feng, Yang; Xia, Lucy: A projection-based conditional dependence measure with applications to high-dimensional undirected graphical models (2020)
  2. Li, Chunlin; Shen, Xiaotong; Pan, Wei: Likelihood ratio tests for a large directed acyclic graph (2020)
  3. Abbruzzo, Antonino; Vujačić, Ivan; Mineo, Angelo M.; Wit, Ernst C.: Selecting the tuning parameter in penalized Gaussian graphical models (2019)
  4. Fop, Michael; Murphy, Thomas Brendan; Scrucca, Luca: Model-based clustering with sparse covariance matrices (2019)
  5. Guo, Xiao; Zhang, Hai; Wang, Yao; Liang, Yong: Structure learning of sparse directed acyclic graphs incorporating the scale-free property (2019)
  6. Kalyagin, Valery A.; Koldanov, Alexander P.; Koldanov, Petr A.; Pardalos, Panos M.: Loss function, unbiasedness, and optimality of Gaussian graphical model selection (2019)
  7. Xu, Kai; Hao, Xinxin: A nonparametric test for block-diagonal covariance structure in high dimension and small samples (2019)
  8. Hong, Younghee; Kim, Choongrak: Recent developments in high dimensional covariance estimation and its related issues, a review (2018)
  9. Li, Peili; Xiao, Yunhai: An efficient algorithm for sparse inverse covariance matrix estimation based on dual formulation (2018)
  10. Sadinle, Mauricio: Bayesian propagation of record linkage uncertainty into population size estimation of human rights violations (2018)
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  12. Yuan, Xiao-Tong; Li, Ping; Zhang, Tong: Gradient hard thresholding pursuit (2018)
  13. Yuen, T. P.; Wong, H.; Yiu, K. F. C.: On constrained estimation of graphical time series models (2018)
  14. Datta, Sagnik; Gayraud, Ghislaine; Leclerc, Eric; Bois, Frederic Y.: \textitGraph_sampler: a simple tool for fully Bayesian analyses of DAG-models (2017)
  15. Hirose, Kei; Fujisawa, Hironori; Sese, Jun: Robust sparse Gaussian graphical modeling (2017)
  16. Koldanov, Petr; Koldanov, Alexander; Kalyagin, Valeriy; Pardalos, Panos: Uniformly most powerful unbiased test for conditional independence in Gaussian graphical model (2017)
  17. Li, Benchong; Li, Yang: A note on faithfulness and total positivity (2017)
  18. Pensar, Johan; Nyman, Henrik; Corander, Jukka: Structure learning of contextual Markov networks using marginal pseudo-likelihood (2017)
  19. Xu, Kai: Testing diagonality of high-dimensional covariance matrix under non-normality (2017)
  20. Lin, Lina; Drton, Mathias; Shojaie, Ali: Estimation of high-dimensional graphical models using regularized score matching (2016)

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