A0620
Title: Estimation of expected Euler characteristic curves of nonstationary smooth random fields
Authors: Dan Cheng - Arizona State University (United States) [presenting]
Abstract: The expected Euler characteristic curve (EEC) summarizes the topology of the excursion sets of a random field above the excursion threshold in terms of its expected Euler characteristic. For large thresholds, the EEC is an excellent approximation for the tail distribution of the supremum of a smooth Gaussian field and has applications in the control of familywise error rate (FWER) and construction of simultaneous confidence bands. Therefore, it is important and valuable to estimate the EEC. Viewed as a function of the excursion threshold, the EEC of a Gaussian-related field is expressed by the Gaussian kinematic formula as a finite sum of known functions multiplied by the Lipschitz Killing curvatures (LKC) of the generating Gaussian field. This transforms the estimation of EEC into estimating LKC. A new method is presented to estimate the LKC as linear projections of pinned Euler characteristic curves obtained from realizations of Gaussian fields. This provides an efficient and accurate tool to estimate the EEC and, hence, high excursion probabilities of Gaussian fields.
