Systems of probability distributions | Actuarial science | Independence (probability theory)
Vine copula
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. Combined with bivariate copulas, regular vines have proven to be a flexible tool in high-dimensional dependence modeling. Copulasare 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 rough known, involving summary indicators and judgment.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 developedand model inference has left the post. Regular vines have proven useful in other problems such as (constrained) sampling of correlation matrices, building non-parametric continuous Bayesian networks. For example, in finance, vine copulas have been shown to effectively model tail risk in portfolio optimization applications. (Wikipedia).
