Probability Density Decomposition for Conditionally Dependent Random Variables Modeled by Vines

By Tim Bedford, Roger M. Cooke. Annals of Mathematics and Artificial Intelligence, 2001

968 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Signal Processing

View Paper: https://www.semanticscholar.org/paper/3308178d3756a19ffc11a1fa3aacf6179cbb4d69

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Citations in the corpus

Multivariate statistical modelling of compound events via pair-copula constructions: analysis of floods in Ravenna (Italy) (2017, positive): “Finally, we underline that this is not the only way to proceed for the conditional simulation (Bedford and Cooke, 2001), but despite the fact that the vine is selected among a fraction of all the existing, it can provide very satisfying results, as we show in this study.”
Selection strategies for regular vine copulae (2013, methodology): “Later a set of linked trees was used in [Bedford and Cooke, 2001, Bedford and Cooke, 2002], which was called a regular (R) vine to identify the pair copulae.”
Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine (2013, methodology): “To classify them Bedford and Cooke (2001, 2002) introduced the graphical model called vine , which is also treated in detail in Kurowicka and Cooke (2006) and Kurowicka and Joe (2011).”
Models for construction of multivariate dependence (2007, background): “This structure was orginally proposed by Joe (1996), and it has later been discussed in detail by Bedford and Cooke (2001, 2002), Kurowicka and Cooke (2006) (sim-”
Parameter estimation for pair-copula constructions (2013, background): “Accordingly, a number of hierarchical, copula-based structures have been proposed, among those the pair-copula construction (PCC) of Joe [22], further studied and considered by Bedford and Cooke [2, 3], Kurowicka and Cooke [30] and Aas et al.”
Pair‐copula constructions for non‐Gaussian DAG models (2012, methodology): “The basic idea of applying PCCs to distributions with certain conditional independence properties goes back to Hanea, Kurowicka, & Cooke (2006) and Kurowicka & Cooke (2006).”
Bayesian model selection for D‐vine pair‐copula constructions (2011, methodology): “Bedford and Cooke (2001, 2002) systemized the approach of Joe (1996) in terms of copula densities by introducing the notion of regular vines. An excellent introduction to regular vines as well as a statistical inference for Gaussian regular vines is given by Kurowicka and Cooke (2006). Aas, Czado, F”
Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50 (2013, methodology): “They were originally proposed by Joe (1996) and further explored and greatly extended by Bedford and Cooke (2001, 2002) and Kurowicka and Cooke (2006).”
Selection of Vine Copulas (2013, background): “[8] showed that the conditioned sets are singletons, and we will therefore refer to edges by their labels {Ce,a,Ce,b|De} =̂ {i(e), j(e)|D(e)}.”
Tail dependence functions and vine copulas (2010, background): “…classifications: 62H20 Keywords: Archimedean copulas Conditional tail D-vine C-vine Extreme value a b s t r a c t Tail dependence and conditional tail dependence functions describe, respectively, the tail probabilities and conditional tail probabilities of a copula at various relative scales.”
Flexible dependence modeling of operational risk losses and its impact on total capital requirements (2014, methodology): “To organize the different decompositions, Bedford and Cooke (2001, 2002) therefore introduced vines as a graphical representation of PCCs. Rather than stating the general definition of vines and vine copulas, we concentrate here on the properties and refer to Kurowicka and Cooke (2006) and Kurowicka”
Multivariate dependence risk and portfolio optimization: An application to mining stock portfolios (2015, methodology): “Vines and Sklar's theorem Graphical vine trees were initially employed by Bedford and Cooke (2001, 2002) as a means to organize and specify multivariate statistical models known as regular vines.”