Ryan Cotsakis
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Ryan Cotsakis has a total of 4 co-authors. Here are the top co-authors by number of shared publications:
- Thomas Opitz
Biostatistics and Spatial Processes, INRAE, Avignon, France
3 shared publications - Elena Bernardino1 shared publication
Elena Di Bernardino
Laboratoire J.A. Dieudonné Université Côte d'Azur Nice France
1 shared publication- Elena Di Bernardino
Laboratoire J.A. Dieudonné, UMR CNRS 7351, Université Côte d’Azur, 06108 Nice, France
1 shared publication
Latest Publications
- 27 January 2024
- Published by Springer Nature in Discrete & Computational Geometry
- Vol. 73 (1) , 92-128
Computable Bounds for the Reach and r-Convexity of Subsets of ${{\mathbb {R}}}^d$- 27 January 2024
- Published by Springer Nature in Discrete & Computational Geometry
- Vol. 73 (1) , 92-128
Computable Bounds for the Reach and r-Convexity of Subsets of ${{\mathbb {R}}}^d$- Open Access
A local statistic for the spatial extent of extreme threshold exceedances
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 excursion-set theory to study distributional properties of the extremal range, propose parametric models and predict the median extremal range at extreme threshold levels. The extremal range captures the rate at which the spatial extent of conditional extreme events scales for increasingly high thresholds, and we relate its distributional properties with the bivariate tail dependence coefficient and the extremal index of time series in classical Extreme-Value Theory. Consistent estimation of the distribution function of the extremal range for stationary random fields is proven. For non-stationary random fields, we implement generalized additive median regression to predict extremal-range maps at very high threshold levels. An application to two large daily temperature datasets, namely reanalyses and climate-model simulations for France, highlights decreasing extremal dependence for increasing threshold levels and reveals strong differences in joint tail decay rates between reanalyses and simulations.
Open AccessA local statistic for the spatial extent of extreme threshold exceedances
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 excursion-set theory to study distributional properties of the extremal range, propose parametric models and predict the median extremal range at extreme threshold levels. The extremal range captures the rate at which the spatial extent of conditional extreme events scales for increasingly high thresholds, and we relate its distributional properties with the bivariate tail dependence coefficient and the extremal index of time series in classical Extreme-Value Theory. Consistent estimation of the distribution function of the extremal range for stationary random fields is proven. For non-stationary random fields, we implement generalized additive median regression to predict extremal-range maps at very high threshold levels. An application to two large daily temperature datasets, namely reanalyses and climate-model simulations for France, highlights decreasing extremal dependence for increasing threshold levels and reveals strong differences in joint tail decay rates between reanalyses and simulations.
- Open Access
- 9 September 2023
- Published by Wiley in Scandinavian Journal of Statistics
- Vol. 51 (1) , 268-301
On the perimeter estimation of pixelated excursion sets of two‐dimensional anisotropic random fields
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 accessible binary digital images of the excursion regions and computes the length of a piecewise linear approximation of the excursion boundary. The estimator is shown to be consistent as the pixel size decreases, without the need of any normalization constant, and with neither assumption of Gaussianity nor isotropy imposed on the underlying random field. In this general framework, even when the domain grows to cover , the estimation error is shown to be of smaller order than the side length of the domain. For affine, strongly mixing random fields, this translates to a multivariate Central Limit Theorem for our estimator when multiple levels are considered simultaneously. Finally, we conduct several numerical studies to investigate statistical properties of the proposed estimator in the finite‐sample data setting.
- 9 September 2023
- Published by Wiley in Scandinavian Journal of Statistics
- Vol. 51 (1) , 268-301
Open AccessOn the perimeter estimation of pixelated excursion sets of two‐dimensional anisotropic random fields
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 accessible binary digital images of the excursion regions and computes the length of a piecewise linear approximation of the excursion boundary. The estimator is shown to be consistent as the pixel size decreases, without the need of any normalization constant, and with neither assumption of Gaussianity nor isotropy imposed on the underlying random field. In this general framework, even when the domain grows to cover , the estimation error is shown to be of smaller order than the side length of the domain. For affine, strongly mixing random fields, this translates to a multivariate Central Limit Theorem for our estimator when multiple levels are considered simultaneously. Finally, we conduct several numerical studies to investigate statistical properties of the proposed estimator in the finite‐sample data setting.
- Open AccessComputable bounds for the reach and $r$-convexity of subsets of $\mathbb{R}^d$The convexity of a set can be generalized to the two weaker notions of reach and $r$-convexity; both describe the regularity of a set's boundary. For any compact subset of $\mathbb{R}^d$, we provide methods for computing upper bounds on these quantities from point cloud data. The bounds converge to the respective quantities as the point cloud becomes dense in the set, and the rate of convergence for the bound on the reach is given under a weak regularity condition. We also introduce the $\beta$-reach, a generalization of the reach that excludes small-scale features of size less than a parameter $\beta\in[0,\infty)$. Numerical studies suggest how the $\beta$-reach can be used in high-dimension to infer the reach and other geometric properties of smooth submanifolds.Open AccessComputable bounds for the reach and $r$-convexity of subsets of $\mathbb{R}^d$The convexity of a set can be generalized to the two weaker notions of reach and $r$-convexity; both describe the regularity of a set's boundary. For any compact subset of $\mathbb{R}^d$, we provide methods for computing upper bounds on these quantities from point cloud data. The bounds converge to the respective quantities as the point cloud becomes dense in the set, and the rate of convergence for the bound on the reach is given under a weak regularity condition. We also introduce the $\beta$-reach, a generalization of the reach that excludes small-scale features of size less than a parameter $\beta\in[0,\infty)$. Numerical studies suggest how the $\beta$-reach can be used in high-dimension to infer the reach and other geometric properties of smooth submanifolds.
- Open AccessComputable bounds for the reach and $r$-convexity of subsets of $\mathbb{R}^d$The convexity of a set can be generalized to the two weaker notions of reach and $r$-convexity; both describe the regularity of a set's boundary. For any compact subset of $\mathbb{R}^d$, we provide methods for computing upper bounds on these quantities from point cloud data. The bounds converge to the respective quantities as the point cloud becomes dense in the set, and the rate of convergence for the bound on the reach is given under a weak regularity condition. We also introduce the $\beta$-reach, a generalization of the reach that excludes small-scale features of size less than a parameter $\beta\in[0,\infty)$. Numerical studies suggest how the $\beta$-reach can be used in high-dimension to infer the reach and other geometric properties of smooth submanifolds.Open AccessComputable bounds for the reach and $r$-convexity of subsets of $\mathbb{R}^d$The convexity of a set can be generalized to the two weaker notions of reach and $r$-convexity; both describe the regularity of a set's boundary. For any compact subset of $\mathbb{R}^d$, we provide methods for computing upper bounds on these quantities from point cloud data. The bounds converge to the respective quantities as the point cloud becomes dense in the set, and the rate of convergence for the bound on the reach is given under a weak regularity condition. We also introduce the $\beta$-reach, a generalization of the reach that excludes small-scale features of size less than a parameter $\beta\in[0,\infty)$. Numerical studies suggest how the $\beta$-reach can be used in high-dimension to infer the reach and other geometric properties of smooth submanifolds.
- Open Access
On the perimeter estimation of pixelated excursion sets of 2D anisotropic random fields
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 empirically accessible binary digital images of the excursion regions and computes the length of a piecewise linear approximation of the excursion boundary. The estimator is shown to be consistent as the pixel size decreases, without the need of any normalization constant, and with neither assumption of Gaussianity nor isotropy imposed on the underlying random field. In this general framework, even when the domain grows to cover $\mathbb R^2$, the estimation error is shown to be of smaller order than the side length of the domain. For affine, strongly mixing random fields, this translates to a multivariate Central Limit Theorem for our estimator when multiple levels are considered simultaneously. Finally, we conduct several numerical studies to investigate statistical properties of the proposed estimator in the finite-sample data setting.Open AccessOn the perimeter estimation of pixelated excursion sets of 2D anisotropic random fields
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 empirically accessible binary digital images of the excursion regions and computes the length of a piecewise linear approximation of the excursion boundary. The estimator is shown to be consistent as the pixel size decreases, without the need of any normalization constant, and with neither assumption of Gaussianity nor isotropy imposed on the underlying random field. In this general framework, even when the domain grows to cover $\mathbb R^2$, the estimation error is shown to be of smaller order than the side length of the domain. For affine, strongly mixing random fields, this translates to a multivariate Central Limit Theorem for our estimator when multiple levels are considered simultaneously. Finally, we conduct several numerical studies to investigate statistical properties of the proposed estimator in the finite-sample data setting.