Excursion Probability of Smooth Multivariate Gaussian Random Fields

• Activity Number: 635
• Type: Topic Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Dan Cheng*+ and Yimin Xiao
• Companies: and Michigan State University
• Keywords: Excursion Probability ; Multivariate Gaussian ; Euler characteristic

Abstract

The excursion probability (or tail probability) of Gaussian random fields has been extensively studied due to the important applications in many areas. But little has been known for the excursion probability of multivariate Gaussian fields, i.e., the probability that every component of the Gaussian fields exceeds a high level. Motivated by the Euler heuristic, we show that as the exceeding level tends to infinity, such probability can be approximated by the expected Euler characteristic of the product of excursion sets generated by the components. Moreover, this approximation is very accurate such that the error is super-exponentially small compared to the major term.