Extremes最新文献

{"title":"Neural Bayes estimation and selection of complex bivariate extremal dependence models.","authors":"L M André, J L Wadsworth, R Huser","doi":"10.1007/s10687-025-00521-8","DOIUrl":"10.1007/s10687-025-00521-8","url":null,"abstract":"<p><p>Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for several models available in the multivariate extremes literature, particularly for the most flexible tail models, including those that interpolate between the two key dependence classes of 'asymptotic dependence' and 'asymptotic independence'. We focus on approaches that leverage neural networks to approximate Bayes estimators. In particular, we explore the properties of neural Bayes estimators for parameter inference for several flexible but computationally expensive models to fit, with a view to aiding their routine implementation. Owing to the absence of likelihood evaluation in the inference procedure, classical information criteria such as the Bayesian information criterion cannot be used to select the most appropriate model. Instead, we propose using neural networks as neural Bayes classifiers for model selection. Our goal is to provide a toolbox for simple, fast fitting and comparison of complex extreme-value dependence models, where the best model is selected for a given data set and its parameters subsequently estimated using neural Bayes estimation. We apply our classifiers and estimators to analyse the pairwise extremal behaviour of changes in horizontal geomagnetic field fluctuations at three different locations.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s10687-025-00521-8.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"29 2","pages":"347-386"},"PeriodicalIF":1.9,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13263241/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148254221","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extreme conformal prediction: Reliable intervals for high-impact events.","authors":"Olivier C Pasche, Henry Lam, Sebastian Engelke","doi":"10.1007/s10687-026-00536-9","DOIUrl":"https://doi.org/10.1007/s10687-026-00536-9","url":null,"abstract":"<p><p>Conformal prediction is a popular method to construct prediction intervals with marginal coverage guarantees from black-box machine learning models. In applications with potentially high-impact events, such as flooding or financial crises, regulators often require very high confidence for such intervals. However, if the desired level of confidence is too large relative to the amount of data used for calibration, then classical conformal methods provide infinitely wide, thus, uninformative prediction intervals. In this paper, we propose a new method to overcome this limitation. We bridge extreme value statistics and conformal prediction to provide reliable and informative prediction intervals with high-confidence coverage, which can be constructed using any black-box extreme quantile regression method. A weighted version of our approach can account for nonstationary data. The advantages of our extreme conformal prediction method are illustrated in a simulation study and in an application to flood risk forecasting.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"29 2","pages":"129-155"},"PeriodicalIF":1.9,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13653964/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149172242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Random coverage from within with variable radii, and Johnson-Mehl cover times.","authors":"Mathew D Penrose, Frankie Higgs","doi":"10.1007/s10687-026-00529-8","DOIUrl":"10.1007/s10687-026-00529-8","url":null,"abstract":"<p><p>Given a compact planar region <b><i>A</i></b> , let <math> <mrow><msub><mi>τ</mi> <mi>A</mi></msub> </mrow> </math> be the (random) time it takes for the Johnson-Mehl tessellation of <b><i>A</i></b> to be complete, i.e. the time for <b><i>A</i></b> to be fully covered by a spatial birth-growth process in <b><i>A</i></b> with seeds arriving as a unit-intensity Poisson point process in <math><mrow><mi>A</mi> <mo>×</mo> <mo>[</mo> <mn>0</mn> <mo>,</mo> <mi>∞</mi> <mo>)</mo></mrow> </math> , where upon arrival each seed grows at unit rate in all directions. We show that if <math><mrow><mi>∂</mi> <mi>A</mi></mrow> </math> is smooth or polygonal then <math><mrow><mi>P</mi> <mo>[</mo> <mrow><mi>π</mi> <msubsup><mi>τ</mi> <mrow><mi>sA</mi></mrow> <mn>3</mn></msubsup> <mo>-</mo> <mn>6</mn> <mo>log</mo> <mi>s</mi> <mo>-</mo> <mn>4</mn> <mo>log</mo> <mo>log</mo> <mi>s</mi> <mo>≤</mo> <mi>x</mi></mrow> <mo>]</mo></mrow> </math> tends to <b>exp</b> <math><mrow><mo>(</mo> <mo>-</mo> <msup><mrow><mo>(</mo> <mfrac><mn>81</mn> <mrow><mn>4</mn> <mi>π</mi></mrow> </mfrac> <mo>)</mo></mrow> <mrow><mn>1</mn> <mo>/</mo> <mn>3</mn></mrow> </msup> <mo>|</mo> <mi>A</mi> <mo>|</mo> <msup><mi>e</mi> <mrow><mo>-</mo> <mi>x</mi> <mo>/</mo> <mn>3</mn></mrow> </msup> <mo>-</mo> <msup><mrow><mo>(</mo> <mfrac><mn>9</mn> <mrow><mn>2</mn> <msup><mi>π</mi> <mn>2</mn></msup> </mrow> </mfrac> <mo>)</mo></mrow> <mrow><mn>1</mn> <mo>/</mo> <mn>3</mn></mrow> </msup> <mo>|</mo> <mi>∂</mi> <mi>A</mi> <mo>|</mo> <msup><mi>e</mi> <mrow><mo>-</mo> <mi>x</mi> <mo>/</mo> <mn>6</mn></mrow> </msup> <mo>)</mo></mrow> </math> in the large- <b><i>s</i></b> limit; the second term in the exponent is due to boundary effects, the importance of which was not recognized in earlier work on this model. We present similar results in higher dimensions (where boundary effects dominate). These results are derived using new results on the asymptotic probability of covering <b><i>A</i></b> with a high-intensity spherical Poisson Boolean model <i>restricted to</i> <b><i>A</i></b> with grains having iid small random radii, which generalize recent work of the first author that dealt only with grains of deterministic radius.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"29 3","pages":"445-494"},"PeriodicalIF":1.9,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13384982/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148551029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generative machine learning for multivariate angular simulation.","authors":"Jakob Benjamin Wessel, Callum J R Murphy-Barltrop, Emma S Simpson","doi":"10.1007/s10687-025-00522-7","DOIUrl":"10.1007/s10687-025-00522-7","url":null,"abstract":"<p><p>With the recent development of new geometric and angular-radial frameworks for multivariate extremes, reliably simulating from angular variables in moderate-to-high dimensions is of increasing importance. Empirical approaches have the benefit of simplicity, and work reasonably well in low dimensions, but as the number of variables increases, they can lack the required flexibility and scalability. Classical parametric models for angular variables, such as the von Mises-Fisher distribution (vMF), provide an alternative. Exploiting finite mixtures of vMF distributions increases their flexibility, but there are cases where, without letting the number of mixture components grow considerably, a mixture model with a fixed number of components is not sufficient to capture the intricate features that can arise in data. Owing to their flexibility, generative deep learning methods are able to capture complex data structures; they therefore have the potential to be useful in the simulation of multivariate angular variables. In this paper, we introduce a range of deep learning approaches for this task, including generative adversarial networks, normalizing flows and flow matching. We assess their performance via a range of metrics, and make comparisons to the more classical approach of using a finite mixture of vMF distributions. The methods are also applied to a metocean data set, with diagnostics indicating strong performance, demonstrating the applicability of such techniques to real-world, complex data structures.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"29 2","pages":"195-243"},"PeriodicalIF":1.9,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13263260/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148254216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Extreme value methods for estimating rare events in Utopia: EVA (2023) conference data challenge: team Lancopula Utopiversity.","authors":"Lídia Maria André, Ryan Campbell, Eleanor D'Arcy, Aiden Farrell, Dáire Healy, Lydia Kakampakou, Conor Murphy, Callum John Rowlandson Murphy-Barltrop, Matthew Speers","doi":"10.1007/s10687-024-00498-w","DOIUrl":"https://doi.org/10.1007/s10687-024-00498-w","url":null,"abstract":"<p><p>To capture the extremal behaviour of complex environmental phenomena in practice, flexible techniques for modelling tail behaviour are required. In this paper, we introduce a variety of such methods, which were used by the Lancopula Utopiversity team to tackle the EVA (2023) Conference Data Challenge. This data challenge was split into four challenges, labelled C1-C4. Challenges C1 and C2 comprise univariate problems, where the goal is to estimate extreme quantiles for a non-stationary time series exhibiting several complex features. For these, we propose a flexible modelling technique, based on generalised additive models, with diagnostics indicating generally good performance for the observed data. Challenges C3 and C4 concern multivariate problems where the focus is on estimating joint probabilities. For challenge C3, we propose an extension of available models in the multivariate literature and use this framework to estimate joint probabilities in the presence of non-stationary dependence. Finally, for challenge C4, which concerns a 50-dimensional random vector, we employ a clustering technique to achieve dimension reduction and use a conditional modelling approach to estimate extremal probabilities across independent groups of variables.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s10687-024-00498-w.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"28 1","pages":"23-45"},"PeriodicalIF":1.1,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11996970/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144018583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Semiparametric approaches for the inference of univariate and multivariate extremes","authors":"Seungwoo Kang, Kyusoon Kim, Youngwook Kwon, Seeun Park, Seoncheol Park, Ha-Young Shin, Joonpyo Kim, Hee-Seok Oh","doi":"10.1007/s10687-024-00497-x","DOIUrl":"https://doi.org/10.1007/s10687-024-00497-x","url":null,"abstract":"<p>In this paper, we present several semiparametric approaches for the inference of univariate and multivariate extremes to resolve the tasks from the EVA (2023) Conference Data Challenge. We implement generalized additive models to capture the flexible relationship for point and interval estimations of the conditional quantiles. We also adopt <span>(L^{p})</span>-quantile to estimate the marginal quantiles of extreme levels. To predict probabilities of multivariate extreme events, we implement conditional methods by Heffernan and Tawn (Royal J. Stat. Soc.: Ser. B (Statistical Methodology) <b>66</b>(3), 497–546, 2004) and Keef et al. (J. Multivar. Anal. <b>115</b>, 396–404, 2013). We further validate predicted models, evaluating their performance scores constructed based on the notion of an equally extreme level of quantiles and cross-validation to select the best estimates to achieve high accuracy. When estimating the excess probability of 50-dimensional data, we cluster variables with high correlation after simple data exploration and combine the results obtained from each cluster. Finally, we also provide post-mortem analysis based on the ground truth.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"32 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182388","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Modern extreme value statistics for Utopian extremes. EVA (2023) Conference Data Challenge: Team Yalla","authors":"Jordan Richards, Noura Alotaibi, Daniela Cisneros, Yan Gong, Matheus B. Guerrero, Paolo Victor Redondo, Xuanjie Shao","doi":"10.1007/s10687-024-00496-y","DOIUrl":"https://doi.org/10.1007/s10687-024-00496-y","url":null,"abstract":"<p>Capturing the extremal behaviour of data often requires bespoke marginal and dependence models which are grounded in rigorous asymptotic theory, and hence provide reliable extrapolation into the upper tails of the data-generating distribution. We present a modern toolbox of four methodological frameworks, motivated by classical extreme value theory, that can be used to accurately estimate extreme exceedance probabilities or the corresponding level in either a univariate or multivariate setting. Our frameworks were used to facilitate the winning contribution of Team Yalla to the EVA (2023) Conference Data Challenge, which was organised for the 13<span>(^text {th})</span> International Conference on Extreme Value Analysis. This competition comprised seven teams competing across four separate sub-challenges, with each requiring the modelling of data simulated from known, yet highly complex, statistical distributions, and extrapolation far beyond the range of the available samples in order to predict probabilities of extreme events. Data were constructed to be representative of real environmental data, sampled from the fantasy country of “Utopia”.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"22 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A utopic adventure in the modelling of conditional univariate and multivariate extremes","authors":"Léo R. Belzile, Arnab Hazra, Rishikesh Yadav","doi":"10.1007/s10687-024-00493-1","DOIUrl":"https://doi.org/10.1007/s10687-024-00493-1","url":null,"abstract":"<p>This paper presents the contribution of Team Yahabe to the EVA (2023) Conference Data Challenge. We tackle the four problems posed by the organizers by revisiting the current and existing literature on conditional univariate and multivariate extremes. We highlight overarching themes linking the four tasks, ranging from model validation at extremely high quantile levels to building customized estimation strategies that leverage model assumptions.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"32 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cross-validation on extreme regions","authors":"Anass Aghbalou, Patrice Bertail, François Portier, Anne Sabourin","doi":"10.1007/s10687-024-00495-z","DOIUrl":"https://doi.org/10.1007/s10687-024-00495-z","url":null,"abstract":"<p>We conduct a non-asymptotic study of the Cross-Validation (CV) estimate of the generalization risk for learning algorithms dedicated to extreme regions of the covariates space. In this context which has recently been analysed from an Extreme Value Analysis perspective, the risk function measures the algorithm’s error given that the norm of the input exceeds a high quantile. The main challenge within this framework is the negligible size of the extreme training sample with respect to the full sample size and the necessity to re-scale the risk function by a probability tending to zero. We open the road to a finite sample understanding of CV for extreme values by establishing two new results: an exponential probability bound on the K-fold CV error and a polynomial probability bound on the leave-p-out CV. Our bounds are sharp in the sense that they match state-of-the-art guarantees for standard CV estimates while extending them to encompass a conditioning event of small probability. We illustrate the significance of our results regarding high dimensional classification in extreme regions via a Lasso-type logistic regression algorithm. The tightness of our bounds is investigated in numerical experiments.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"22 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Gaussian triangular arrays in the case of strong dependence","authors":"Evgeniy Savinov","doi":"10.1007/s10687-024-00491-3","DOIUrl":"https://doi.org/10.1007/s10687-024-00491-3","url":null,"abstract":"<p>We investigate the behavior of extreme values in Gaussian triangular arrays under strong dependence conditions. By extending previous results, we establish conditions for convergence to a mixture of Gaussian and Gumbel distributions without requiring stationarity. Our findings offer insights into the application of these models, particularly for analyzing air ozone concentrations.</p>","PeriodicalId":49274,"journal":{"name":"Extremes","volume":"9 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142182393","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}