Structural analysis of spatio‐temporal threshold exceedances

Angulo, J. M.; Madrid, Ana E.

doi:10.1002/env.1018

Cited by 11 publications

(6 citation statements)

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“…Recurrence and persistence, among others, are examples of such characteristics which provide information about the distribution patterns of extremal events. Formally, these concepts are intimately related to the geometrical characteristics of the excursion sets defined by threshold exceedances over a given (bounded) domain (Angulo and Madrid, ). Given the fragmented nature of threshold exceedance sets, depending on the variation properties that are inherited by sample paths from the probabilistic structure of a random field and on the threshold considered, marked point processes provide a powerful framework for the analysis of their structural properties (Madrid et al ., ).…”

Section: Discussion On the Paper By Ehm Gneiting Jordan And Krügermentioning

confidence: 99%

Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations and Forecast Rankings

Ehm

Gneiting

Jordan³

et al. 2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

153

205

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Summary. In the practice of point prediction, it is desirable that forecasters receive a directive in the form of a statistical functional. For example, forecasters might be asked to report the mean or a quantile of their predictive distributions. When evaluating and comparing competing forecasts, it is then critical that the scoring function used for these purposes be consistent for the functional at hand, in the sense that the expected score is minimized when following the directive. We show that any scoring function that is consistent for a quantile or an expectile functional can be represented as a mixture of elementary or extremal scoring functions that form a linearly parameterized family. Scoring functions for the mean value and probability forecasts of binary events constitute important examples. The extremal scoring functions admit appealing economic interpretations of quantiles and expectiles in the context of betting and investment problems. The Choquet-type mixture representations give rise to simple checks of whether a forecast dominates another in the sense that it is preferable under any consistent scoring function. In empirical settings it suffices to compare the average scores for only a finite number of extremal elements. Plots of the average scores with respect to the extremal scoring functions, which we call Murphy diagrams, permit detailed comparisons of the relative merits of competing forecasts.

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Section: Discussion On the Paper By Ehm Gneiting Jordan And Krügermentioning

confidence: 99%

Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations and Forecast Rankings

Ehm

Gneiting

Jordan³

et al. 2016

Journal of the Royal Statistical Society Series B: Statistical Methodology

153

205

View full text Add to dashboard Cite

show abstract

“…ESs indicate where the variables of interest are above some critical limit. Identifying ESs is important in several environmental applications (Angulo & Madrid, 2010; French & Sain, 2013). Let l be the critical limit of the system.…”

Section: Autonomous Sampling Designsmentioning

confidence: 99%

Using an autonomous underwater vehicle with onboard stochastic advection‐diffusion models to map excursion sets of environmental variables

2021

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New robotic sensor platforms have computing resources that enable a rich set of tasks for adaptive monitoring of the environment. But to substantially augment the toolbox of environmental sensing, such platforms must be embedded with realistic statistical models and coherent methodologies for designing experiments and assimilating the data. In this article, we develop myopic and hybrid strategies for autonomous underwater vehicle sampling in space and time. These strategies are based on a stochastic advection‐diffusion Gaussian process model for the mine tailings concentration in a Norwegian fjord, and the goal is to monitor the excursion set (ES) of high concentrations. Closed form expressions for the expected misclassification probabilities of the ES enable real‐time operation on board the autonomous vehicle, and this is used to guide the spatio‐temporal sampling. Simulation studies show that the suggested strategies outperform other approaches that either (i) simplify the models for spatio‐temporal variation, or (ii) simplify the design criterion. A field test shows how autonomous underwater sampling is useful for refining an initial stochastic advection‐diffusion model. These experiments further show that the vehicle can adapt to focus on regions with intermediate concentrations where it is natural to improve the ES prediction.

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“…In many applications, the excursion set of a random field (i.e., the subset of the observation domain on which the random field exceeds a certain threshold) is observed—or partially observed—and its geometry can be used to make meaningful inferences about the underlying field. Such techniques have been used in disciplines such as astrophysics (Ade et al, 2016; Gott et al, 1990), brain imaging (Worsley et al, 1992), and environmental sciences (Angulo & Madrid, 2010; Frölicher et al, 2018; Lhotka & Kyselỳ, 2015). In certain cases, for example in landscape ecology, land‐use analysis, and statistical modeling, understanding the geometry of excursions is of primary importance (Bolin & Lindgren, 2015; McGarigal, 1995; Nagendra et al, 2004).…”

Section: Introductionmentioning

confidence: 99%

On the perimeter estimation of pixelated excursion sets of two‐dimensional anisotropic random fields

Cotsakis,

Di Bernardino,

Opitz

2023

Scandinavian J Statistics

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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 ℝ2 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 ℝ2, 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.This article is protected by copyright. All rights reserved.

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Structural analysis of spatio‐temporal threshold exceedances

Cited by 11 publications

References 50 publications

Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations and Forecast Rankings

Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations and Forecast Rankings

Using an autonomous underwater vehicle with onboard stochastic advection‐diffusion models to map excursion sets of environmental variables

On the perimeter estimation of pixelated excursion sets of two‐dimensional anisotropic random fields

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