OPITZ , Thomas

We introduce the extremal range, a local statistic for studying the spatial extent of extreme events in random fields on R2. Conditioned on exceedance of a high threshold at a location s, the extremal range at s is the random variable defined as the smallest distance from s to a location where there is a non-exceedance. We leverage tools from...

Geometric properties of excursion sets above a given quantile level provide meaningful theoretical and statistical characterizations for stochastic processes defined on Euclidean domains. Many theoretical results have been obtained for excursions of Gaussian processes and include expected values of the so-called Lipschitz-Killing curvatures...

We are interested in creating statistical methods to provide informative summaries of random fields through the geometry of their excursion sets.To this end, we introduce an estimator for the length of the perimeter of excursion sets of random fields on $\mathbb R^2$ observed over regular square tilings. The proposed estimator acts on the...

We are interested in creating statistical methods to provide informative summaries of random fields through the geometry of their excursion sets. To this end, we introduce an estimator for the length of the perimeter of excursion sets of random fields on observed over regular square tilings. The proposed estimator acts on the empirically...

We introduce the extremal range, a local statistic for studying the spatial extent of extreme events in random fields on $\mathbb{R}^d$. Conditioned on exceedance of a high threshold at a location s, the extremal range at $s$ is the random variable defined as the smallest distance from $s\in\mathbb{R}^d$ to a location where there is a...