Thursday, March 28, 2019

Thursday, March 28, 2019 — 4:00 PM EDT

Excursion Probabilities and Geometric Properties of Multivariate Gaussian Random Fields

Excursion probabilities of Gaussian random fields have many applications in statistics (e.g., scanning statistic and control of false discovery rate (FDR)) and in other areas. The study of excursion probabilities has had a long history and is closely related to geometry of Gaussian random fields. In recent years, important developments have been made in both probability and statistics.

In this talk, we consider the excursion probabilities of bivariate Gaussian random fields with non-smooth (or fractal) sample functions and study their geometric properties and excursion probabilities. Important classes of multivariate Gaussian random fields are those stationary with Matérn cross-covariance functions [Gneiting, Kleiber, and Schlather (2010)] and operator fractional Brownian motions which are operator-self-similar with stationary increments.

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