Academic literature on the topic 'Extremal dependence modeling'
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Journal articles on the topic "Extremal dependence modeling"
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Barro, Diakarya. "Extremal Dependence Modeling with Spatial and Survival Distributions." Journal of Mathematics Research 9, no. 1 (January 23, 2017): 127. http://dx.doi.org/10.5539/jmr.v9n1p127.
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This paper investigates some properties of dependence of extreme values distributions both in survival and spatial context. Specifically, we prospose a spatial Extremal dependence coefficient for survival distributions. Madogram is characterized in bivariate case and multivariate survival function and the underlying hazard distributions are given in a risky context.
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Huser, Raphaël, and Jennifer L. Wadsworth. "Modeling Spatial Processes with Unknown Extremal Dependence Class." Journal of the American Statistical Association 114, no. 525 (June 28, 2018): 434–44. http://dx.doi.org/10.1080/01621459.2017.1411813.
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Mallam, Hassane Abba, Natatou Dodo Moutari, Barro Diakarya, and Saley Bisso. "Extremal Copulas and Tail Dependence in Modeling Stochastic Financial Risk." European Journal of Pure and Applied Mathematics 14, no. 3 (August 5, 2021): 1057–81. http://dx.doi.org/10.29020/nybg.ejpam.v14i3.3951.
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These last years the stochastic modeling became essential in financial risk management related to the ownership and valuation of financial products such as assets, options and bonds. This paper presents a contribution to the modeling of stochastic risks in finance by using both extensions of tail dependence coefficients and extremal dependance structures based on copulas. In particular, we show that when the stochastic behavior of a set of risks can be modeled by a multivariate extremal process a corresponding form of the underlying copula describing theirdependence is determined. Moreover a new tail dependence measure is proposed and properties of this measure are established.
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Apputhurai, P., and A. G. Stephenson. "Accounting for uncertainty in extremal dependence modeling using Bayesian model averaging techniques." Journal of Statistical Planning and Inference 141, no. 5 (May 2011): 1800–1807. http://dx.doi.org/10.1016/j.jspi.2010.11.038.
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Ressel, Paul. "Stable tail dependence functions – some basic properties." Dependence Modeling 10, no. 1 (January 1, 2022): 225–35. http://dx.doi.org/10.1515/demo-2022-0114.
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Abstract We prove some important properties of the extremal coefficients of a stable tail dependence function (“STDF”) and characterise logistic and some related STDFs. The well known sufficient conditions for composebility of logistic STDFs are shown to be also necessary.
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Chen, Zaoli, and Gennady Samorodnitsky. "Extremal clustering under moderate long range dependence and moderately heavy tails." Stochastic Processes and their Applications 145 (March 2022): 86–116. http://dx.doi.org/10.1016/j.spa.2021.12.001.
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Olinda, R. A., J. Blanchet, C. A. C. dos Santos, V. A. Ozaki, and P. J. Ribeiro Jr. "Spatial extremes modeling applied to extreme precipitation data in the state of Paraná." Hydrology and Earth System Sciences Discussions 11, no. 11 (November 17, 2014): 12731–64. http://dx.doi.org/10.5194/hessd-11-12731-2014.
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Abstract. Most of the mathematical models developed for rare events are based on probabilistic models for extremes. Although the tools for statistical modeling of univariate and multivariate extremes are well developed, the extension of these tools to model spatial extremes includes an area of very active research nowadays. A natural approach to such a modeling is the theory of extreme spatial and the max-stable process, characterized by the extension of infinite dimensions of multivariate extreme value theory, and making it possible then to incorporate the existing correlation functions in geostatistics and therefore verify the extremal dependence by means of the extreme coefficient and the Madogram. This work describes the application of such processes in modeling the spatial maximum dependence of maximum monthly rainfall from the state of Paraná, based on historical series observed in weather stations. The proposed models consider the Euclidean space and a transformation referred to as space weather, which may explain the presence of directional effects resulting from synoptic weather patterns. This method is based on the theorem proposed for de Haan and on the models of Smith and Schlather. The isotropic and anisotropic behavior of these models is also verified via Monte Carlo simulation. Estimates are made through pairwise likelihood maximum and the models are compared using the Takeuchi Information Criterion. By modeling the dependence of spatial maxima, applied to maximum monthly rainfall data from the state of Paraná, it was possible to identify directional effects resulting from meteorological phenomena, which, in turn, are important for proper management of risks and environmental disasters in countries with its economy heavily dependent on agribusiness.
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Li, Jiayi, Zhiyan Cai, Yixuan Liu, and Chengxiu Ling. "Extremal Analysis of Flooding Risk and Its Catastrophe Bond Pricing." Mathematics 11, no. 1 (December 27, 2022): 114. http://dx.doi.org/10.3390/math11010114.
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Catastrophic losses induced by natural disasters are receiving growing attention because of the severe increases in their magnitude and frequency. We first investigated the extreme tail behavior of flood-caused economic losses and maximum point precipitation based on the peaks-over-threshold method and point process (PP) model and its extreme tail dependence. We found that both maximum point precipitation and direct economic losses are well-modeled by the PP approach with certain tail dependence. These findings were further utilized to design a layered compensation insurance scheme using estimated value-at-risk (VaR) and conditional VaR (CVaR) among all stakeholders. To diversify the higher level of losses due to extreme precipitation, we designed a coupon paying catastrophe bond triggered by hierarchical maximum point precipitation level, based on the mild assumption on the independence between flood-caused risk and financial risk. The pricing sensitivity was quantitatively analyzed in terms of the tail risk of the flood disaster and the distortion magnitude and the market risk in Wang’s transform. Our trigger process was carefully designed using a compound Poisson process, modeling both the frequency and the layered intensity of flood disasters. Lastly, regulations and practical suggestions are provided regarding the flood risk prevention and warning.
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Saunina, A. Yu, V. R. Nikitenko, A. A. Chistyakov, M. A. Zvaizgne, A. R. Tameev, and A. E. Aleksandrov. "Analytic Modeling of the of J–V Characteristics of Quantum Dot-Based Photovoltaic Cells." International Journal of Nanoscience 18, no. 03n04 (April 2, 2019): 1940083. http://dx.doi.org/10.1142/s0219581x19400830.
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An analytic model of [Formula: see text]–[Formula: see text] characteristics of photovoltaic devices based on quantum dot (QD) solids is developed. The model yields the upper estimation of the power conversion efficiency and predicts its extremal dependence on the diffusion length of excitons. The predictive power of our model is approved by the comparison with the experimental data for PbS QD-based solar cells.
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Ferreira, Helena, and Marta Ferreira. "The stopped clock model." Dependence Modeling 10, no. 1 (January 1, 2022): 48–57. http://dx.doi.org/10.1515/demo-2022-0101.
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Abstract The extreme value theory presents specific tools for modeling and predicting extreme phenomena. In particular, risk assessment is often analyzed through measures for tail dependence and high values clustering. Despite technological advances allowing an increasingly larger and more efficient data collection, there are sometimes failures in the records, which causes difficulties in statistical inference, especially in the tail where data are scarcer. In this article, we present a model with a simple and intuitive failures scheme, where each record failure is replaced by the last record available. We will study its extremal behavior with regard to local dependence and high values clustering, as well as the temporal dependence on the tail.
Dissertations / Theses on the topic "Extremal dependence modeling"
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Kereszturi, Monika. "Assessing and modelling extremal dependence in spatial extremes." Thesis, Lancaster University, 2017. http://eprints.lancs.ac.uk/86369/.
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Offshore structures, such as oil platforms and vessels, must be built such that they can withstand extreme environmental conditions (e.g., high waves and strong winds) that may occur during their lifetime. This means that it is essential to quantify probabilities of the occurrence of such extreme events. However, a difficulty arises in that there are very limited data available at these levels. The statistical field of extreme value theory provides asymptotically motivated models for extreme events, hence allowing extrapolation to very rare events. In addition to the risk to a single site, we are also interested in the joint risk of multiple offshore platforms being affected by the same extreme event. In order to understand joint extremal behaviour for two or more locations, the spatial dependence between the different locations must be considered. Extremal dependence between two locations can be of two types: asymptotic independence (AI) when the extremes at the two sites are unlikely to occur together, and asymptotic dependence (AD) when it is possible for both sites to be affected simultaneously. For finite samples it is often difficult to determine which type of dependence the data are more consistent with. In a large ocean basin it is reasonable to expect both of these features to be present, with some close by locations AD, with the dependence decreasing with distance, and some far apart locations AI. In this thesis we develop new diagnostic tools for distinguishing between AD and AI and illustrate these on North Sea wave height data. We also investigate how extremal dependence changes with direction and find evidence for spatial anisotropy in our data set. The most widely used spatial models assume asymptotic dependence or perfect independence between sites, which is often unrealistic in practice. Models that attempt to capture both AD and AI exist, but they are difficult to implement in practice due to their complexity and they are restricted in the forms of AD and AI they can model. In this thesis we introduce a family of bivariate distributions that exhibits all the required features of short, medium and long range extremal dependence required for pairwise dependence modelling in spatial applications.
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Lecei, Ivan [Verfasser]. "Modelling extremal dependence / Ivan Lecei." Ulm : Universität Ulm, 2018. http://d-nb.info/1173249745/34.
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Johnson, Jill Suzanne. ""Modelling Dependence in Extreme Environmental Events"." Thesis, University of Newcastle upon Tyne, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.525050.
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Navarrete, Miguel A. Ancona. "Dependence modelling and spatial prediction for extreme values." Thesis, Lancaster University, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369658.
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Eriksson, Kristofer. "Risk Measures and Dependence Modeling in Financial Risk Management." Thesis, Umeå universitet, Institutionen för fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-85185.
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In financial risk management it is essential to be able to model dependence in markets and portfolios in an accurate and efficient way. A high positive dependence between assets in a portfolio can be devastating, especially in times of crises, since losses will most likely occur at the same time in all assets for such a portfolio. The dependence is therefore directly linked to the risk of the portfolio. The risk can be estimated by several different risk measures, for example Value-at-Risk and Expected shortfall. This paper studies some different ways to measure risk and model dependence, both in a theoretical and empirical way. The main focus is on copulas, which is a way to model and construct complex dependencies. Copulas are a useful tool since it allows the user to separately specify the marginal distributions and then link them together with the copula. However, copulas can be quite complex to understand and it is not trivial to know which copula to use. An implemented copula model might give the user a "black-box" feeling and a severe model risk if the user trusts the model too much and is unaware of what is going. Another model would be to use the linear correlation which is also a way to measure dependence. This is an easier model and as such it is believed to be easier for all users to understand. However, linear correlation is only easy to understand in the case of elliptical distributions, and when we move away from this assumption (which is usually the case in financial data), some clear drawbacks and pitfalls become present. A third model, called historical simulation, uses the historical returns of the portfolio and estimate the risk on this data without making any parametric assumptions about the dependence. The dependence is assumed to be incorporated in the historical evolvement of the portfolio. This model is very easy and very popular, but it is more limited than the previous two models to the assumption that history will repeat itself and needs much more historical observations to yield good results. Here we face the risk that the market dynamics has changed when looking too far back in history. In this paper some different copula models are implemented and compared to the historical simulation approach by estimating risk with Value-at-Risk and Expected shortfall. The parameters of the copulas are also investigated under calm and stressed market periods. This information about the parameters is useful when performing stress tests. The empirical study indicates that it is difficult to distinguish the parameters between the stressed and calm market period. The overall conclusion is; which model to use depends on our beliefs about the future distribution. If we believe that the distribution is elliptical then a correlation model is good, if it is believed to have a complex dependence then the user should turn to a copula model, and if we can assume that history will repeat itself then historical simulation is advantageous.
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Singh, Abhay Kumar. "Modelling Extreme Market Risk - A Study of Tail Related Risk Measures." Thesis, Edith Cowan University, Research Online, Perth, Western Australia, 2011. https://ro.ecu.edu.au/theses/417.
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Market risk modelling is one of the most dynamic domains in finance. Risk is the uncertainty that affects the values of assets in the system in an unknown fashion causing fluctuations in their values and in investment outcomes. Market risk is defined as the losses due to fluctuations in the prices of financial assets which are caused by changing market conditions. Market risk modelling comprises tools and techniques which quantify the risk associated with financial instruments. Risk quantification is necessary to devise strategies such as hedging or diversification against the risk, to avoid severe losses. With the recent financial market events like the Global Financial Crisis, there is a need to evaluate the traditional risk return relationships presented in Asset Pricing models and more sophisticated risk modelling tools like Value at Risk (VaR). Along with Asset Pricing and VaR modelling another important risk issue between financial assets is the asymptotic tail dependence, which plays a vital role in accurate risk measurement in portfolio selection and hedging amongst other considerations. The usual measure of dependence, the Pearson Correlation coefficient works on the assumption of normality in the data distribution and hence is unable to capture the tail dependence between financial assets which is an important characteristic for tail risk modelling. The research presented in this dissertation models the risk quantification techniques of Asset Pricing, VaR modelling and Tail dependence, with the more sophisticated statistical tools of Quantile Regression and Extreme Value Theory (EVT), which are particularly useful in modelling the tail behaviour of the distributions. The research targets four broad objectives to evaluate extreme risk and dependence measures in the Australian stock market which are realised with the robust techniques of Quantile Regression and EVT. The thesis comprises six chapters with chapter-1 introducing the thesis presenting the driving motivations for the research and the four major objectives (which are detailed in individual chapters following chapter-1) along with the contribution of the research and finally chapter-6 presenting the conclusion. The structure of rest of the thesis is also outlined in chapter-1.
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Boulin, Alexis. "Partitionnement des variables de séries temporelles multivariées selon la dépendance de leurs extrêmes." Electronic Thesis or Diss., Université Côte d'Azur, 2024. http://www.theses.fr/2024COAZ5039.
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Dans un grand éventail d'applications allant des sciences du climat à la finance, des événements extrêmes avec une probabilité loin d'être négligeable peuvent se produire, entraînant des conséquences désastreuses. Les extrêmes d'évènements climatiques tels que le vent, la température et les précipitations peuvent profondément affecter les êtres humains et les écosystèmes, entraînant des événements tels que des inondations, des glissements de terrain ou des vagues de chaleur. Lorsque l'emphase est mise sur l'étude de variables mesurées dans le temps sur un grand nombre de stations ayant une localisation spécifique, comme les variables mentionnées précédemment, le partitionnement de variables devient essentiel pour résumer et visualiser des tendances spatiales, ce qui est crucial dans l'étude des événements extrêmes. Cette thèse explore plusieurs modèles et méthodes pour partitionner les variables d'un processus stationnaire multivarié, en se concentrant sur les dépendances extrémales.Le chapitre 1 présente les concepts de modélisation de la dépendance via les copules, fondamentales pour la dépendance extrême. La notion de variation régulière est introduite, essentielle pour l'étude des extrêmes, et les processus faiblement dépendants sont abordés. Le partitionnement est discuté à travers les paradigmes de séparation-proximité et de partitionnement basé sur un modèle. Nous abordons aussi l'analyse non-asymptotique pour évaluer nos méthodes dans des dimensions fixes.Le chapitre 2 est à propos de la dépendance entre valeurs maximales est cruciale pour l'analyse des risques. Utilisant la fonction de copule de valeur extrême et le madogramme, ce chapitre se concentre sur l'estimation non paramétrique avec des données manquantes. Un théorème central limite fonctionnel est établi, démontrant la convergence du madogramme vers un processus Gaussien tendu. Des formules pour la variance asymptotique sont présentées, illustrées par une étude numérique.Le chapitre 3 propose les modèles asymptotiquement indépendants par blocs (AI-blocs) pour le partitionnement de variables, définissant des clusters basés sur l'indépendance des maxima. Un algorithme est introduit pour récupérer les clusters sans spécifier leur nombre à l'avance. L'efficacité théorique de l'algorithme est démontrée, et une méthode de sélection de paramètre basée sur les données est proposée. La méthode est appliquée à des données de neurosciences et environnementales, démontrant son potentiel.Le chapitre 4 adapte des techniques de partitionnement pour analyser des événements extrêmes composites sur des données climatiques européennes. Les sous-régions présentant une dépendance des extrêmes de précipitations et de vitesse du vent sont identifiées en utilisant des données ERA5 de 1979 à 2022. Les clusters obtenus sont spatialement concentrés, offrant une compréhension approfondie de la distribution régionale des extrêmes. Les méthodes proposées réduisent efficacement la taille des données tout en extrayant des informations cruciales sur les événements extrêmes.Le chapitre 5 propose une nouvelle méthode d'estimation pour les matrices dans un modèle linéaire à facteurs latents, où chaque composante d'un vecteur aléatoire est exprimée par une équation linéaire avec des facteurs et du bruit. Contrairement aux approches classiques basées sur la normalité conjointe, nous supposons que les facteurs sont distribués selon des distributions de Fréchet standards, ce qui permet une meilleure description de la dépendance extrémale. Une méthode d'estimation est proposée garantissant une solution unique sous certaines conditions. Une borne supérieure adaptative pour l'estimateur est fournie, adaptable à la dimension et au nombre de facteursIn a wide range of applications, from climate science to finance, extreme events with a non-negligible probability can occur, leading to disastrous consequences. Extremes in climatic events such as wind, temperature, and precipitation can profoundly impact humans and ecosystems, resulting in events like floods, landslides, or heatwaves. When the focus is on studying variables measured over time at numerous specific locations, such as the previously mentioned variables, partitioning these variables becomes essential to summarize and visualize spatial trends, which is crucial in the study of extreme events. This thesis explores several models and methods for partitioning the variables of a multivariate stationary process, focusing on extreme dependencies.Chapter 1 introduces the concepts of modeling dependence through copulas, which are fundamental for extreme dependence. The notion of regular variation, essential for studying extremes, is introduced, and weakly dependent processes are discussed. Partitioning is examined through the paradigms of separation-proximity and model-based clustering. Non-asymptotic analysis is also addressed to evaluate our methods in fixed dimensions.Chapter 2 study the dependence between maximum values is crucial for risk analysis. Using the extreme value copula function and the madogram, this chapter focuses on non-parametric estimation with missing data. A functional central limit theorem is established, demonstrating the convergence of the madogram to a tight Gaussian process. Formulas for asymptotic variance are presented, illustrated by a numerical study.Chapter 3 proposes asymptotically independent block (AI-block) models for partitioning variables, defining clusters based on the independence of maxima. An algorithm is introduced to recover clusters without specifying their number in advance. Theoretical efficiency of the algorithm is demonstrated, and a data-driven parameter selection method is proposed. The method is applied to neuroscience and environmental data, showcasing its potential.Chapter 4 adapts partitioning techniques to analyze composite extreme events in European climate data. Sub-regions with dependencies in extreme precipitation and wind speed are identified using ERA5 data from 1979 to 2022. The obtained clusters are spatially concentrated, offering a deep understanding of the regional distribution of extremes. The proposed methods efficiently reduce data size while extracting critical information on extreme events.Chapter 5 proposes a new estimation method for matrices in a latent factor linear model, where each component of a random vector is expressed by a linear equation with factors and noise. Unlike classical approaches based on joint normality, we assume factors are distributed according to standard Fréchet distributions, allowing a better description of extreme dependence. An estimation method is proposed, ensuring a unique solution under certain conditions. An adaptive upper bound for the estimator is provided, adaptable to dimension and the number of factors
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Ayari, Samia. "Nonparametric estimation of the dependence function for multivariate extreme value distributions." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4078.
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Dans cette thèse, nous abordons l'estimation non paramétrique de la fonction de dépendance des distributions multivariées à valeurs extrêmes. Dans une première partie, on adopte l’hypothèse classique stipulant que les variables aléatoires sont indépendantes et identiquement distribuées (i.i.d). Plusieurs estimateurs non paramétriques sont comparés pour une fonction de dépendance trivariée de type logistique dans deux différents cas. Dans le premier cas, on suppose que les fonctions marginales sont des distributions généralisées à valeurs extrêmes. La distribution marginale est remplacée par la fonction de répartition empirique dans le deuxième cas. Les résultats des simulations Monte Carlo montrent que l'estimateur Gudendorf-Segers (Gudendorf et Segers, 2011) est plus efficient que les autres estimateurs pour différentes tailles de l’échantillon. Dans une deuxième partie, on ignore l’hypothèse i.i.d vue qu’elle n'est pas vérifiée dans l'analyse des séries temporelles. Dans le cadre univarié, on examine le comportement extrêmal d'un modèle autorégressif Gaussien stationnaire. Dans le cadre multivarié, on développe un nouveau théorème qui porte sur la convergence asymptotique de l'estimateur de Pickands vers la fonction de dépendance théorique. Ce fondement théorique est vérifié empiriquement dans les cas d’indépendance et de dépendance asymptotique. Dans la dernière partie de la thèse, l'estimateur Gudendorf-Segers est utilisé pour modéliser la structure de dépendance des concentrations extrêmes d’ozone observées dans les stations qui enregistrent des dépassements de la valeur guide et limite de la norme Tunisienne de la qualité d'air NT.106.04In this thesis, we investigate the nonparametric estimation of the dependence function for multivariate extreme value distributions. Firstly, we assume independent and identically distributed random variables (i.i.d). Several nonparametric estimators are compared for a trivariate dependence function of logistic type in two different cases. In a first analysis, we suppose that marginal functions are generalized extreme value distributions. In a second investigation, we substitute the marginal function by the empirical distribution function. Monte Carlo simulations show that the Gudendorf-Segers (Gudendorf and Segers, 2011) estimator outperforms the other estimators for different sample sizes. Secondly, we drop the i.i.d assumption as it’s not verified in time series analysis. Considering the univariate framework, we examine the extremal behavior of a stationary Gaussian autoregressive process. In the multivariate setting, we prove the asymptotic consistency of the Pickands dependence function estimator. This theoretical finding is confirmed by empirical investigations in the asymptotic independence case as well as the asymptotic dependence case. Finally, the Gudendorf-Segers estimator is used to model the dependence structure of extreme ozone concentrations in locations that record several exceedances for both guideline and limit values of the Tunisian air quality standard NT.106.04
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Kyselá, Eva. "Modelling portfolios with heavy-tailed risk factors." Master's thesis, Vysoká škola ekonomická v Praze, 2015. http://www.nusl.cz/ntk/nusl-264017.
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The thesis aims to investigate some of the approaches to modelling portfolio returns with heavy-tailed risk factors. It first elaborates on the univariate time series models, and compares the benchmark model (GARCH with Student t innovations or its GJR extension) predictive performance with its two competitors, the EVT-GARCH model and the Markov-Switching Multifractal (MSM) model. The motivation of EVT extension of GARCH specification is to use a more proper distribution of the innovations, based on the empirical distribution function. The MSM is one of the best performing models in the multifractal literature, a markov-switching model which is unique by its parsimonious specification and variability. The performance of these models is assessed with Mincer-Zarnowitz regressions as well as by comparison of quality of VaR and expected shortfall predictions, and the empirical analysis shows that for the risk management purposes the EVT-GARCH dominates the benchmark as well as the MSM. The second part addresses the dependence structure modelling, using the Gauss and t-copula to model the portfolio returns and compares the result with the classic variance-covariance approach, concluding that copulas offer a more realistic estimates of future extreme quantiles.
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Schulz, Thorsten [Verfasser], Matthias [Akademischer Betreuer] [Gutachter] Scherer, Griselda [Gutachter] Deelstra, and Ralf [Gutachter] Werner. "Stochastic dependencies in derivative pricing: Decoupled BNS-volatility, sequential modeling of jumps, and extremal WWR / Thorsten Schulz ; Gutachter: Matthias Scherer, Griselda Deelstra, Ralf Werner ; Betreuer: Matthias Scherer." München : Universitätsbibliothek der TU München, 2017. http://d-nb.info/1147566003/34.
Full textBooks on the topic "Extremal dependence modeling"
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Gao, Yanhong, and Deliang Chen. Modeling of Regional Climate over the Tibetan Plateau. Oxford University Press, 2017. http://dx.doi.org/10.1093/acrefore/9780190228620.013.591.
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The modeling of climate over the Tibetan Plateau (TP) started with the introduction of Global Climate Models (GCMs) in the 1950s. Since then, GCMs have been developed to simulate atmospheric dynamics and eventually the climate system. As the highest and widest international plateau, the strong orographic forcing caused by the TP and its impact on general circulation rather than regional climate was initially the focus. Later, with growing awareness of the incapability of GCMs to depict regional or local-scale atmospheric processes over the heterogeneous ground, coupled with the importance of this information for local decision-making, regional climate models (RCMs) were established in the 1970s. Dynamic and thermodynamic influences of the TP on the East and South Asia summer monsoon have since been widely investigated by model. Besides the heterogeneity in topography, impacts of land cover heterogeneity and change on regional climate were widely modeled through sensitivity experiments.In recent decades, the TP has experienced a greater warming than the global average and those for similar latitudes. GCMs project a global pattern where the wet gets wetter and the dry gets drier. The climate regime over the TP covers the extreme arid regions from the northwest to the semi-humid region in the southeast. The increased warming over the TP compared to the global average raises a number of questions. What are the regional dryness/wetness changes over the TP? What is the mechanism of the responses of regional changes to global warming? To answer these questions, several dynamical downscaling models (DDMs) using RCMs focusing on the TP have recently been conducted and high-resolution data sets generated. All DDM studies demonstrated that this process-based approach, despite its limitations, can improve understandings of the processes that lead to precipitation on the TP. Observation and global land data assimilation systems both present more wetting in the northwestern arid/semi-arid regions than the southeastern humid/semi-humid regions. The DDM was found to better capture the observed elevation dependent warming over the TP. In addition, the long-term high-resolution climate simulation was found to better capture the spatial pattern of precipitation and P-E (precipitation minus evapotranspiration) changes than the best available global reanalysis. This facilitates new and substantial findings regarding the role of dynamical, thermodynamics, and transient eddies in P-E changes reflected in observed changes in major river basins fed by runoff from the TP. The DDM was found to add value regarding snowfall retrieval, precipitation frequency, and orographic precipitation.Although these advantages in the DDM over the TP are evidenced, there are unavoidable facts to be aware of. Firstly, there are still many discrepancies that exist in the up-to-date models. Any uncertainty in the model’s physics or in the land information from remote sensing and the forcing could result in uncertainties in simulation results. Secondly, the question remains of what is the appropriate resolution for resolving the TP’s heterogeneity. Thirdly, it is a challenge to include human activities in the climate models, although this is deemed necessary for future earth science. All-embracing further efforts are expected to improve regional climate models over the TP.
Book chapters on the topic "Extremal dependence modeling"
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Ortego, María I., Juan J. Egozcue, and Raimon Tolosana-Delgado. "Modeling Extremal Dependence Using Copulas. Application to Rainfall Data." In Lecture Notes in Earth System Sciences, 53–56. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-32408-6_13.
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Praprom, Chakorn, and Songsak Sriboonchitta. "Extreme Value Copula Analysis of Dependences between Exchange Rates and Exports of Thailand." In Modeling Dependence in Econometrics, 187–99. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-03395-2_12.
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Boonyanuphong, Phattanan, and Songsak Sriboonchitta. "An Analysis of Volatility and Dependence between Rubber Spot and Futures Prices Using Copula-Extreme Value Theory." In Modeling Dependence in Econometrics, 431–44. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-03395-2_27.
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Kaewkheaw, Mutita, Pisit Leeahtam, and Chukiat Chaiboosri. "An Analysis of Relationship between Gold Price and U.S. Dollar Index by Using Bivariate Extreme Value Copulas." In Modeling Dependence in Econometrics, 455–62. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-03395-2_29.
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Coles, Stuart. "Extremes of Dependent Sequences." In An Introduction to Statistical Modeling of Extreme Values, 92–104. London: Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-3675-0_5.
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Taylor, John, and Jay Larson. "Resolution Dependence in Modeling Extreme Weather Events." In Computational Science — ICCS 2001, 204–11. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/3-540-45545-0_29.
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Weissman, Ishay. "On Some Dependence Measures for Multivariate Extreme Value Distributions." In Advances in Mathematical and Statistical Modeling, 171–80. Boston: Birkhäuser Boston, 2008. http://dx.doi.org/10.1007/978-0-8176-4626-4_12.
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"Nonparametric Estimation of Extremal Dependence Anna Kiriliouk, Johan Segers, and Michał Warchoł." In Extreme Value Modeling and Risk Analysis, 373–96. Chapman and Hall/CRC, 2016. http://dx.doi.org/10.1201/b19721-21.
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Smith, Elizabeth L., and David Walshaw. "Modelling Bivariate Extremes in a Region." In Bayesian Statistics 7, 681–90. Oxford University PressOxford, 2003. http://dx.doi.org/10.1093/oso/9780198526155.003.0048.
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Abstract Practitioners of extreme value methodology have been slow to accept the Bayesian paradigm, and the initial work that has been carried out in recent years has reflected the history of the classical approach, in concentrating solely on univariate problems. In this paper we take a first step towards balancing the substantial frequentist literature on multivariate extreme value inference by considering problems of bivariate inference from a Bayesian point of view. We relate the bivariate case to inference problems for extremes of environmental variables recorded at a number of locations in a spatial region. We show how inference for bivariate extreme value models can be implemented using an MCMC scheme, and compare two popular model families. We then select one of these families for use in a practical example involving rainfall data. We employ prior information on marginal behavior of extremes constructed from carefully elicited expert beliefs, while prior beliefs about the dependence parameter relate the strength of dependence inversely to the distance between locations, thus exploiting the spatial aspect inherent in the inference problem. We briefly discuss how our ongoing work in this area will lead to a spatial model which enables inference at a particular location of interest to be improved through the model for bivariate extremal dependencies with other locations. We conclude with a pointer to inference for max-stable process models, which are being developed by the authors to address the problems involved in truly multivariate inference.
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"Extreme Dependence Models." In Extreme Value Modeling and Risk Analysis, 345–72. Chapman and Hall/CRC, 2016. http://dx.doi.org/10.1201/b19721-20.
Full textConference papers on the topic "Extremal dependence modeling"
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Towe, Ross, Emma Eastoe, Jonathan Tawn, Yanyun Wu, and Philip Jonathan. "The Extremal Dependence of Storm Severity, Wind Speed and Surface Level Pressure in the Northern North Sea." In ASME 2013 32nd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/omae2013-10154.
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Characterising the joint distribution of extremes of significant wave height and wind speed is critical for reliable design and assessment of marine structures. The extremal dependence of pairs of oceanographic variables can be characterised using one of a number of summary statistics, which describe the two different types of extremal dependence. Quantifying the type of extremal dependence is an essential pre-requisite to joint or spatial extreme value modelling, and ensures that appropriate model forms are employed. We estimate extremal dependence between storm peak significant wave height and storm peak wind speed (Hs, WS) for locations in a region of the northern North Sea. However, since the extremal dependence itself may vary with storm direction, we introduce new covariate-dependent forms of the extremal dependence measures that account for the direction of the storm. We discuss the implications of all of the estimates for marine design, including specification of joint design criteria for extended spatial domains, and statistical downscaling to incorporate the effects of climate change on design specification.
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"Evaluating extremal dependence in stock markets using Extreme Value Theory." In 19th International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand (MSSANZ), Inc., 2011. http://dx.doi.org/10.36334/modsim.2011.d6.singh2.
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McDonald, Andrew, Pang-Ning Tan, and Lifeng Luo. "COMET Flows: Towards Generative Modeling of Multivariate Extremes and Tail Dependence." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/462.
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Normalizing flows—a popular class of deep generative models—often fail to represent extreme phenomena observed in real-world processes. In particular, existing normalizing flow architectures struggle to model multivariate extremes, characterized by heavy-tailed marginal distributions and asymmetric tail dependence among variables. In light of this shortcoming, we propose COMET (COpula Multivariate ExTreme) Flows, which decompose the process of modeling a joint distribution into two parts: (i) modeling its marginal distributions, and (ii) modeling its copula distribution. COMET Flows capture heavy-tailed marginal distributions by combining a parametric tail belief at extreme quantiles of the marginals with an empirical kernel density function at mid-quantiles. In addition, COMET Flows capture asymmetric tail dependence among multivariate extremes by viewing such dependence as inducing a low-dimensional manifold structure in feature space. Experimental results on both synthetic and real-world datasets demonstrate the effectiveness of COMET flows in capturing both heavy-tailed marginals and asymmetric tail dependence compared to other state-of-the-art baseline architectures. All code is available at https://github.com/andrewmcdonald27/COMETFlows.
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Wada, Ryota, Philip Jonathan, Takuji Waseda, and Shejun Fan. "Estimating Extreme Waves in the Gulf of Mexico Using a Simple Spatial Extremes Model." In ASME 2019 38th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2019. http://dx.doi.org/10.1115/omae2019-95442.
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Abstract We seek to characterize the behavior of extreme waves in the Gulf of Mexico, using a 109 year-long wave hindcast (GOMOS). The largest waves in this region are driven by strong winds from hurricanes. Design of offshore production systems requires the estimation of extreme metocean conditions corresponding to return periods from 1 year to 10,000 years and beyond. For extrapolation to long return periods, estimation using data for around 100 years from a single location will incur large uncertainties. Approaches such as spatial pooling, cyclone track-shifting and explicit track modeling have been proposed to alleviate this problem. The underlying problem in spatial pooling is the aggregation of dependent data and hence underestimation of uncertainty using naïve analysis; techniques such as block-bootstrapping can be used to inflate uncertainties to more realistic levels. The usefulness of cyclone track-shifting or explicit track modeling is dependent on the appropriateness of the physical assumptions underpinning such a model. In this paper, we utilize a simple spatial statistical model for extreme value estimation of significant wave height under tropical cyclones, known as STM-E, proposed in Wada et al. (2018). The STM-E model was developed to characterize extreme waves offshore Japan, also dominated by tropical cyclones. The method relies on the estimation of two distributions from a sample of data, namely the distribution of spatio-temporal maximum (STM) and the exposure (E). In the current work, we apply STM-E to extreme wave analysis in Gulf of Mexico. The STM-E estimate provides a parsimonious spatially-smooth distribution of extreme waves, with smaller uncertainties per location compared to estimates using data from a single location. We also discuss the estimated characteristics of extreme wave environments in this region.
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Vanem, Erik, Øystein Lande, and Elias Fekhari. "A Simulation Study on the Usefulness of the Bernstein Copula for Statistical Modeling of Metocean Variables." In ASME 2024 43rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/omae2024-121159.
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Abstract Probabilistic modelling of relevant environmental variables are crucial for the safe design and operation of marine structures. Using metocean data, a joint model of several variables can be estimated, including their dependence structure. Often, a conditional model is assumed for this, but recently the non-parametric Bernstein copula has been suggested as an alternative tool to model such dependencies. As a non-parametric technique, it is very flexible and often provides excellent goodness-of-fit to data with different dependencies. However, non-parametric techniques are prone to over-fitting and generalizability might be challenging. Moreover, care should be taken when using such models for extrapolation. In this paper, a simple simulation study will be presented that has investigated the usefulness of the Bernstein copula in modeling joint metocean variables. First, data have been generated from a known parametric joint distribution model. Then, a joint model based on the Bernstein copula is fitted to a subset of these data. Data simulated from the Bernstein-based models are then compared to data from the initial model. A particular focus will be put on how the model captures the dependencies in the extremes.
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Barbariol, Francesco, Alvise Benetazzo, Filippo Bergamasco, Sandro Carniel, and Mauro Sclavo. "Stochastic Space-Time Extremes of Wind Sea States: Validation and Modeling." In ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/omae2014-23997.
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Damages and accidents occurred to offshore structures and routing ships raise questions about adequacy of conventional time domain analysis of short-crested sea waves. Indeed, experimental and field evidence showed that during such wave states, typical of storms, the maximum sea surface elevation gathered at a single point in time, i.e. the time extreme, tends to underestimate the actual maximum that occurs over a surrounding area, i.e. the space-time extreme. Recently, stochastic models for the prediction of multidimensional Gaussian random fields maxima, e.g. Piterbarg’s theorem and Adler and Taylor’s approach, have been applied to ocean waves statistics, permitting to extend extreme value analysis from time to space-time domain. In this paper, we present analytical and numerical approaches aimed at supporting applicability of such models, which is limited by the knowledge of directional spectrum parameters. Firstly, we validate stochastic models against stereo-photogrammetric measurements of surface wave fields. Then, we investigate the dependence of space-time extremes upon physical parameters (wind speed, fetch length, current speed) in the context of analytical spectral formulations, i.e. Pierson-Moskowitz and JONSWAP, and by using spectral numerical wave modeling. To this end, we developed two sets of closed formulae and a modified version of the SWAN model to calculate parameters of analytical and arbitrary directional spectra, respectively. Finally, we present preliminary results of a 3 years Mediterranean Sea hindcast as a first step towards operational forecasts of space-time extremes.
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Wada, Ryota, Philip Jonathan, and Takuji Waseda. "Spatial Features of Extreme Waves in Gulf of Mexico." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-19190.
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Abstract Extreme value analysis of significant wave height using data from a single location often incurs large uncertainty due to small sample size. Including wave data from nearby locations increases sample size at the risk of introducing dependency between extreme events and hence violating modelling assumptions. In this work, we consider extreme value analysis of spatial wave data from the 109-year GOMOS wave hindcast for the Gulf of Mexico, seeking to incorporate the effects of spatial dependence in a simple but effective manner. We demonstrate that, for estimation of return values at a given location, incorporation of data from a circular disk region with radius of approximately 5° (long.-lat.), centred at the location of interest, provides an appropriate basis for extreme value analysis using the STM-E approach of Wada et al. (2018).
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Yu, Hang, Zheng Choo, Justin Dauwels, Philip Jonathan, and Qiao Zhou. "Modeling spatially-dependent extreme events with Markov random field priors." In 2012 IEEE International Symposium on Information Theory - ISIT. IEEE, 2012. http://dx.doi.org/10.1109/isit.2012.6283503.
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Vanem, Erik. "Stochastic Models for Long-Term Prediction of Extreme Waves: A Literature Survey." In ASME 2010 29th International Conference on Ocean, Offshore and Arctic Engineering. ASMEDC, 2010. http://dx.doi.org/10.1115/omae2010-20076.
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This paper presents a literature survey on time-dependent statistical modelling of extreme waves. The focus is twofold: on statistical modelling of extreme waves and time-dependent statistical modelling. The first part will consist of a thorough literature review of statistical modelling of extreme waves and wave parameters. The second part will focus on statistical modelling of time- and space-dependent variables in a more general sense, and will focus on the methodology and models used also in other relevant application areas. It was found that limited effort has been put on developing statistical models for waves incorporating spatial and long-term temporal variability and it is suggested that model improvements could be achieved by adopting approaches from other application areas. Finally, a review of projections of future extreme wave climate is presented.
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Mackay, E. B. L., C. J. R. Murphy-Barltrop, and P. Jonathan. "The SPAR Model: A New Paradigm for Multivariate Extremes. Application to Joint Distributions of Metocean Variables." In ASME 2024 43rd International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2024. http://dx.doi.org/10.1115/omae2024-130932.
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Abstract This paper presents the application of a new multivariate extreme value model for the estimation of metocean variables. The model requires fewer assumptions about the forms of the margins and dependence structure compared to existing approaches, and provides a flexible and rigorous framework for modelling multi-variate extremes. The method involves a transformation of variables to polar coordinates. The tail of the radial variable is then modelled using the generalised Pareto distribution, with parameters conditional on angle, providing a natural extension of uni-variate theory to multivariate problems. The resulting model is referred to as the semi-parametric angular-radial (SPAR) model. We consider the estimation of the joint distributions of (1) wave height and wave period, and (2) wave height and wind speed. We show that the SPAR model provides a good fit to the observations in terms of both the marginal distributions and dependence structures. The use of the SPAR model for estimating long-term extreme responses of offshore structures is discussed, using some simple response functions for floating structures and an offshore wind turbine with monopile foundation. We show that the SPAR model is able to accurately reproduce response distributions, and provides a realistic quantification of uncertainty.
Reports on the topic "Extremal dependence modeling"
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Furman, Alex, Jan Hopmans, Shmuel Assouline, Jirka Simunek, and Jim Richards. Soil Environmental Effects on Root Growth and Uptake Dynamics for Irrigated Systems. United States Department of Agriculture, February 2011. http://dx.doi.org/10.32747/2011.7592118.bard.
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Root water uptake is perhaps the most important unknown in the mass balance of hydrological and agricultural systems. The understanding and the ability to predict root uptake and the way it is influence by environmental conditions has great potential in increasing water and fertilizer use efficiency and allowing better control of water and contaminant leach towards groundwater. This BARD supported research is composed of several components, including a) intensive laboratory work for the quantification of root uptake and the way it is controlled by environmental conditions; b) development of tools for laboratory and field use that can help in sensing very low water fluxes and water content, which is a necessity for studying root uptake; c) development of capabilities to model compensated root uptake; and d) development of a database that will allow calibration of such a model. In addition some auxiliary research was performed as reported later. Some of the components, and especially the modeling and the HPP development, were completed in the framework of the project and even published in the international literature. The completed components provide a modeling environment that allows testing root compensated uptake modeling, a tool that is extremely important for true mechanistic understanding of root uptake and irrigation design that is based on mechanistic and not partially based myth. The new button HPP provides extended level of utilization of this important tool. As discussed below, other components did not get to maturity stage during the period of the project, but comprehensive datasets were collected and will be analyzed in the near future. A comprehensive dataset of high temporal and spatial resolution water contents for two different setups was recorded and should allow us understanding f the uptake at these fine resolutions. Additional important information about root growth dynamics and its dependence in environmental conditions was achieved in both Israel and the US. Overall, this BARD supported project provided insight on many important phenomena related to root uptake and to high resolution monitoring in the vadose zone. Although perhaps not to the level that we initially hoped for, we achieved better understanding of the related processes, better modeling capabilities, and better datasets that will allow continuation of this effort in the near future.
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Oliynyk, Kateryna, and Matteo Ciantia. Application of a finite deformation multiplicative plasticity model with non-local hardening to the simulation of CPTu tests in a structured soil. University of Dundee, December 2021. http://dx.doi.org/10.20933/100001230.
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In this paper an isotropic hardening elastoplastic constitutive model for structured soils is applied to the simulation of a standard CPTu test in a saturated soft structured clay. To allow for the extreme deformations experienced by the soil during the penetration process, the model is formulated in a fully geometric non-linear setting, based on: i) the multiplicative decomposition of the deformation gradient into an elastic and a plastic part; and, ii) on the existence of a free energy function to define the elastic behaviour of the soil. The model is equipped with two bonding-related internal variables which provide a macroscopic description of the effects of clay structure. Suitable hardening laws are employed to describe the structure degradation associated to plastic deformations. The strain-softening associated to bond degradation usually leads to strain localization and consequent formation of shear bands, whose thickness is dependent on the characteristics of the microstructure (e.g, the average grain size). Standard local constitutive models are incapable of correctly capturing this phenomenon due to the lack of an internal length scale. To overcome this limitation, the model is framed using a non-local approach by adopting volume averaged values for the internal state variables. The size of the neighbourhood over which the averaging is performed (characteristic length) is a material constant related to the microstructure which controls the shear band thickness. This extension of the model has proven effective in regularizing the pathological mesh dependence of classical finite element solutions in the post-localization regime. The results of numerical simulations, conducted for different soil permeabilities and bond strengths, show that the model captures the development of plastic deformations induced by the advancement of the cone tip; the destructuration of the clay associated with such plastic deformations; the space and time evolution of pore water pressure as the cone tip advances. The possibility of modelling the CPTu tests in a rational and computationally efficient way opens a promising new perspective for their interpretation in geotechnical site investigations.