Global InformationVine copula information
A vine is a graphical tool for labeling constraints in high-dimensional probability distributions. A regular vine is a special case for which all constraints are two-dimensional or conditional two-dimensional. Regular vines generalize trees, and are themselves specializations of Cantor tree.[1]
Combined with bivariate copulas, regular vines have proven to be a flexible tool in high-dimensional dependence modeling. Copulas [2][3] are multivariate distributions with uniform univariate margins. Representing a joint distribution as univariate margins plus copulas allows the separation of the problems of estimating univariate distributions from the problems of estimating dependence. This is handy in as much as univariate distributions in many cases can be adequately estimated from data, whereas dependence information is roughly unknown, involving summary indicators and judgment.[4][5] Although the number of parametric multivariate copula families with flexible dependence is limited, there are many parametric families of bivariate copulas. Regular vines owe their increasing popularity to the fact that they leverage from bivariate copulas and enable extensions to arbitrary dimensions. Sampling theory and estimation theory for regular vines are well developed [6][7] and model inference has left the post .[8][9][7] Regular vines have proven useful in other problems such as (constrained) sampling of correlation matrices,[10][11] building non-parametric continuous Bayesian networks.[12][13]
For example, in finance, vine copulas have been shown to effectively model tail risk in portfolio optimization applications.[14]
- ^ Bedford, T.J.; Cooke, R.M. (2002). "Vines — a new graphical model for dependent random variables". Annals of Statistics. 30 (4): 1031–1068. CiteSeerX 10.1.1.26.8965. doi:10.1214/aos/1031689016.
- ^ Joe, H. (1997). Multivariate Models and Dependence Concepts. London: Chapman & Hall.
- ^ Nelsen, R.B. (2006). An Introduction to Copulas, 2nd ed. New York: Springer.
- ^ Kraan, B.C.P.; Cooke, R.M. (2000). "Processing expert judgements in accident consequence modeling". Radiation Protection Dosimetry. 90 (3): 311–315. doi:10.1093/oxfordjournals.rpd.a033153.
- ^ Ale, B.J.M.; Bellamy, L.J.; van der Boom, R.; Cooper, J.; Cooke, R.M.; Goossens, L.H.J.; Hale, A.R.; Kurowicka, D.; Morales, O.; Roelen, A.L.C.; Spouge, J. (2009). "Further development of a Causal model for Air Transport Safety (CATS): Building the mathematical heart". Reliability Engineering and System Safety Journal. 94 (9): 1433–1441. doi:10.1016/j.ress.2009.02.024.
- ^ Kurowicka, D.; Cooke, R.M. (2007). "Sampling algorithms for generating joint uniform distributions using the vine-copula method". Computational Statistics and Data Analysis. 51 (6): 2889–2906. doi:10.1016/j.csda.2006.11.043.
- ^ a b Aas, K.; Czado, C.; Frigessi, A.; Bakken, H. (2009). "Pair-copula constructions of multiple dependence". Insurance: Mathematics and Economics. 44 (2): 182–198. CiteSeerX 10.1.1.61.3984. doi:10.1016/j.insmatheco.2007.02.001. S2CID 18320750.
- ^ Kurowicka, D.; Cooke, R.M. (2006). Uncertainty Analysis with High Dimensional Dependence Modelling. Wiley.
- ^ Kurowicka, D.; Cooke, R.M.; Callies, U. (2007). "Vines inference". Brazilian Journal of Probability and Statistics.
- ^ Lewandowski, D.; Kurowicka, D.; Joe, H. (2009). "Generating random correlation matrices based on vines and extended onion method". Journal of Multivariate Analysis. 100 (9): 1989–2001. doi:10.1016/j.jmva.2009.04.008.
- ^ Kurowicka, D. (2014). "Generating random correlation matrices based on vines and extended onion method". Joint Density of Correlations in the Correlation Matrix with Chordal Sparsity Patterns. 129 (C): 160–170. doi:10.1016/j.jmva.2014.04.006.
- ^ Hanea, A.M. (2008). Algorithms for Non-parametric Bayesian Belief Nets (Ph.D.). Delft Institute of Applied Mathematics, Delft University of Technology.
- ^ Hanea, A.M.; Kurowicka, D.; Cooke, R.M.; Ababei, D.A. (2010). "Mining and visualising ordinal data with non-parametric continuous BBNs". Computational Statistics and Data Analysis. 54 (3): 668–687. doi:10.1016/j.csda.2008.09.032.
- ^ Low, R.K.Y.; Alcock, J.; Faff, R.; Brailsford, T. (2013). "Canonical vine copulas in the context of modern portfolio management: Are they worth it?". Journal of Banking & Finance. 37 (8): 3085–3099. doi:10.1016/j.jbankfin.2013.02.036. S2CID 154138333.