Modeling Bivariate Gauge Functions using Bezier Curves

Joint work with Brian Reich (NCSU), Ben Shaby (CSU), and Dan Cooley (CSU).

A recent trend in (bivariate) extremes analysis focuses on the use of gauge functions which models the entire tail dependence in a geometric manner. Most common measures of tail dependence can also be directly extracted from the form of this gauge function. Current methods usually need to assume a parametric form for the gauge function, which is quite restrictive. We propose the use of Bezier curves which can model complex shapes, and use it in a Bayesian framework to get a full posterior distribution (with uncertainty) of the gauge functions.

Our approach is flexible, robust, and can identify different regimes of asymptotic behavior that the joint tail exhibits.