Semiparametric Estimation of the Shape of the Limiting Bivariate Point Cloud

Thomas M. Menino Convention & Exhibition Center 

Understanding and modeling the relationship between the extremes of multiple variables is crucial for mitigating the risk associated with high impact phenomena. The study of geometric extremes, where extremal dependence properties are inferred from the deterministic limiting shapes of scaled sample clouds, provides an exciting approach to modeling the tail behavior of multivariate data. These shapes, termed limit sets, link several popular extremal dependence modelling frameworks. We propose a novel Bayesian approach to model limit sets for bivariate data. We directly model the shape of the limit set using Bezier splines, which allow flexible and parsimonious specification of shapes in two dimensions. We fit the Bezier splines to data in pseudo-polar coordinates using Markov chain Monte Carlo sampling, utilizing a limiting approximation to the conditional likelihood of the radii given angles. Two applications are presented to showcase the usefulness of limit sets for studying tail dependence in environmental data: extremal dependence for fire weather variables in Santa Ana, California, and for air pollution monitoring data in the US.

Bayesian inference

Environmental modeling

Multivariate extremes 

Section on Statistics and the Environment