Representing Sparse Gaussian DAGs as Sparse R-Vines Allowing for Non-Gaussian Dependence

References

• Aas, K., Czado, C., Frigessi, A., and Bakken, H. (2009), “Pair-Copula Constructions of Multiple Dependence,” Insurance, Mathematics and Economics, 44, 182–198.
   Web of Science ®Google Scholar
• Andersson, S. A., and Perlman, M. D. (1998), “Normal Linear Regression Models With Recursive Graphical Markov Structure,” Journal of Multivariate Analysis, 66, 133–187.
   Web of Science ®Google Scholar
• Bauer, A., and Czado, C. (2016), “Pair-Copula Bayesian Networks,” Journal of Computational and Graphical Statistics, 25, 1248–1271.
   Web of Science ®Google Scholar
• Bauer, A., Czado, C., and Klein, T. (2012), “Pair-Copula Constructions for Non-Gaussian DAG Models,” Canadian Journal of Statistics, 40, 86–109.
   Web of Science ®Google Scholar
• Bedford, T., and Cooke, R. (2001), “Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines,” Annals of Mathematics and Artificial Intelligence, 32, 245–268.
   Web of Science ®Google Scholar
• ——— (2002), “Vines—A New Graphical Model for Dependent Random Variables,” Annals of Statistics, 30, 1031–1068.
   Web of Science ®Google Scholar
• Brechmann, E., and Czado, C. (2013), “Risk Management with High-Dimensional Vine Copulas: An Analysis of the Euro Stoxx 50,” Statistics & Risk Modeling, 30, 307–342.
   Google Scholar
• Brechmann, E. C., and Joe, H. (2014), “Parsimonious Parameterization of Correlation Matrices Using Truncated Vines and Factor Analysis,” Computational Statistics & Data Analysis, 77, 233–251.
   Web of Science ®Google Scholar
• Csardi, G., and Nepusz, T. (2006), “The Igraph Software Package for Complex Network Research,” InterJournal Complex Systems, 1695, 1–9.
   Google Scholar
• Czado, C. (2010), “Pair-Copula Constructions of Multivariate Copulas,” in Workshop on Copula Theory and its Applications, eds. F. Durante, W. Härdle, P. Jaworki, and T. Rychlik, Dordrecht: Springer, pp. 93–107.
   Google Scholar
• Czado, C., Brechmann, E., and Gruber, L. (2013), “Selection of Vine Copulas,” in Copulae in Mathematical and Quantitative Finance, eds. P. Jaworski, F. Durante, and W. Härdle, New York: Springer, pp. 17–37.
   Google Scholar
• Dißmann, J., Brechmann, E., Czado, C., and Kurowicka, D. (2013), “Selecting and Estimating Regular Vine Copulae and Application to Financial Returns,” Computational Statistics and Data Analysis, 52, 52–59.
   Google Scholar
• Elidan, G. (2010), “Copula Bayesian Networks,” in Advances in Neural Information Processing Systems (Vol. 23), eds. J. Lafferty, C. Williams, J. Shawe-Taylor, R. Zemel, and A. Culotta, Curran Associates, Inc., pp. 559–567
   Google Scholar
• Fan, Y., and Tang, C. Y. (2013), “Tuning Parameter Selection in High Dimensional Penalized Likelihood,” Journal of the Royal Statistical Society, Series B, 75, 531–552.
   Google Scholar
• Gruber, L., and Czado, C. (2015a), “Bayesian Model Selection of Regular Vine Copulas,” available at https://www.statistics.ma.tum.de/fileadmin/w00bdb/www/LG/bayes-vine.pdf
   Google Scholar
• ——— (2015b), “Sequential Bayesian Model Selection of Regular Vine Copulas,” Bayesian Analysis, 10, 937–963.
   Web of Science ®Google Scholar
• Hobæk Haff, I., Aas, K., Frigessi, A., and Graziani, V. L. (2016), “Structure Learning in Bayesian Networks using Regular Vines,” Computational Statistics and Data Analysis, 101, 186–208.
   Web of Science ®Google Scholar
• Joe, H. (1996), “Families of m-Variate Distributions with Given Margins and m(m − 1)/2 Bivariate Dependence Parameters,” in Distributions with Fixed Marginals and Related Topics, eds. L. Rüschendorf, B. Schweizer, and M. D. Taylor, Hayward, CA: Institute of Mathematical Statistics, pp. 120–141.
   Google Scholar
• Koller, D., and Friedman, N. (2009), Probabilistic Graphical Models: Principles and Techniques (1st ed.), Cambridge, MA: MIT Press.
   Google Scholar
• Kullback, S., and Leibler, R. (1951), “On Information and Sufficiency,” Annals of Mathematical Statistics, 22, 79–86.
   Google Scholar
• Kurowicka, D., and Cooke, R. (2006), Uncertainty Analysis and High Dimensional Dependence Modelling (1st ed.), Chicester: Wiley.
   Google Scholar
• Kurowicka, D., and Joe, H. (2011), Dependence Modeling - Handbook on Vine Copulae, Singapore: World Scientific Publishing Co.
   Google Scholar
• Lauritzen, S. L. (1996), Graphical Models (1st ed.), Oxford: Oxford University Press.
   Google Scholar
• Peters, J., and Bühlmann, P. (2014), “Identifiability of Gaussian Structural Equation Models with Equal Error Variances,” Biometrika, 101, 219–228.
   Web of Science ®Google Scholar
• Pircalabelu, E., Claeskens, G., and Gijbels, I. (2017), “Copula Directed Acyclic Graphs,” Statistics and Computing, 27, 55–78.
   Web of Science ®Google Scholar
• Prim, R. C. (1957), “Shortest Connection Networks and Some Generalizations,” Bell System Technical Journal, 36, 1389–1401.
   Google Scholar
• R Core Team (2017), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Schepsmeier, U., Stöber, J., Brechmann, E. C., Graeler, B., Nagler, T., and Erhardt, T. (2016), VineCopula: Statistical Inference of Vine Copulas, R Package Version 2.1.1.
   Google Scholar
• Scutari, M. (2010), “Learning Bayesian Networks with the bnlearn R Package,” Journal of Statistical Software, 35, 1–22.
   PubMed Web of Science ®Google Scholar
• Sklar, A. (1959), “Fonctions dé Repartition á n Dimensions et Leurs Marges,” Publications de l’Institut de Statistique de L’Université de Paris, 8, 229–231.
   Google Scholar
• Stöber, J., Joe, H., and Czado, C. (2013), “Simplified Pair Copula Constructions-Limitations and Extensions,” Journal of Multivariate Analysis, 119, 101–118.
   Web of Science ®Google Scholar
• Whittaker, J. (1990), Graphical Models in Applied Multivariate Statistics (1st ed.), Chicester: Wiley.
   Google Scholar
• Wickham, H. (2009), ggplot2: Elegant Graphics for Data Analysis, New York: Springer-Verlag.
   Google Scholar