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arxiv: 2412.13453 · v6 · submitted 2024-12-18 · 📊 stat.ME

Modeling extremal dependence in multivariate and spatial problems: a practical perspective

Boris Beranger , Simone A. Padoan This is my paper

Pith reviewed 2026-05-23 07:15 UTC · model grok-4.3

classification 📊 stat.ME
keywords extremal dependencemultivariate extremesspatial extremesR packageextreme value theoryrisk assessmentenvironmental applicationsfinancial extremes
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The pith

The ExtremalDep R package supplies instructions for analyzing multivariate and spatial extreme events after minimal background.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper supplies a brief introduction to multivariate and spatial extreme value methods and then shows how to apply them using the ExtremalDep R package. It demonstrates the package through several real-world applications drawn from environmental sciences and finance. A sympathetic reader would value this because it addresses the practical difficulty of assessing risks from events that exceed the range of available data when multiple variables or spatial structure are involved. The package is positioned as the main vehicle that turns the theory into usable steps.

Core claim

After a minimal background on the statistical methodologies, the ExtremalDep R package supplies a toolbox that lets users analyse multivariate and spatial extreme events, with the instructions and code validated through several real-world applications.

What carries the argument

The ExtremalDep R package toolbox for fitting models of extremal dependence in multivariate and spatial settings.

If this is right

  • Users can extrapolate risks beyond observed data while accounting for dependence among multiple variables.
  • Spatial extreme events can be modelled and assessed with the same package functions.
  • Professionals in environmental sciences and finance can perform the analyses by following the supplied instructions.
  • The package reduces the expertise barrier for routine risk assessments that involve extremes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same instructional style could be applied to other R packages that implement specialised statistical models.
  • The examples could be extended to include simulation-based validation of the fitted models.
  • Users might combine the package output with existing spatial mapping tools to visualise results more directly.
  • Future package updates could add support for newer dependence measures not covered in the current applications.

Load-bearing premise

The real-world applications shown in the paper correctly implement and validate the multivariate and spatial extreme value methods without hidden data-selection choices that affect the reported fits.

What would settle it

Re-running the package on the paper's example datasets produces fits that materially differ from those reported or fail standard checks for extremal dependence.

Figures

Figures reproduced from arXiv: 2412.13453 by Boris Beranger, Simone A. Padoan.

Figure 1
Figure 1. Figure 1: Estimated angular densities from the H¨usler-Reiss model. [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Left panel shows the approximate posterior distribution of tail probability with [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Clusters of 35 weather stations and their estimated extremal coefficients in dimen [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: De-trended and de-seasonalised times series of monthly-maxima of log-returns of [PITH_FULL_IMAGE:figures/full_fig_p016_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Diagnostic plots for the MCMC algorithm. Left and centre columns focus on the [PITH_FULL_IMAGE:figures/full_fig_p017_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Outputs of the summary.ExtDep (left) and returns (right) functions. defined in (2.17), for extreme values specified by y. The argument plot calls the plot routine on the object x to visualize such probabilities as long as y defines a square grid and data adds the relevant datapoints. Usage of the summary and returns functions is provided below with graphical outputs presented in [PITH_FULL_IMAGE:figures/f… view at source ↗
Figure 7
Figure 7. Figure 7: Estimated Pickands dependence function (left) and angular density (middle and [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Observed (black dots) differential of pressure (mbar) and daily-maximum wind [PITH_FULL_IMAGE:figures/full_fig_p021_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Estimated probabilities to belong to the failure regions [PITH_FULL_IMAGE:figures/full_fig_p021_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Top row: posterior mean estimate (dotted line) and 90% credible interval (grey) [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Estimated marginal location (left), scale (middle) and shape (right) parameters. [PITH_FULL_IMAGE:figures/full_fig_p026_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Simulation from the fitted extremal skew- [PITH_FULL_IMAGE:figures/full_fig_p027_12.png] view at source ↗
read the original abstract

From environmental sciences to finance, there is a growing demand for methods that can assess the risks of extreme events beyond those observed in available data. Extrapolating extreme events beyond the range of the data is not obvious. Risk assessments are often further complicated by the need to account for multiple variables simultaneously. Extreme value theory provides important tools for the analysis of multivariate or spatial extreme events, but these are not easily accessible to professionals without appropriate expertise. This article provides a minimal background on multivariate and spatial extremes and gives simple yet thorough instructions on how to analyse them using the R package ExtremalDep. After briefly introducing the statistical methodologies, we focus on road testing the package's toolbox through several real-world applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper supplies a concise introduction to multivariate and spatial extreme-value methods and demonstrates their implementation through the ExtremalDep R package on several real-data examples drawn from environmental and financial contexts.

Significance. If the reported applications correctly implement the methods and fully document modeling choices, the work provides accessible, reproducible guidance that can increase uptake of extremal-dependence tools among practitioners; the package itself constitutes a concrete deliverable.

major comments (2)
  1. [Applications / real-world examples] Applications section (real-world examples): the manuscript does not report the precise threshold-selection procedure or block-maxima definitions used for each dataset, nor does it include sensitivity checks on these choices; because extremal-dependence parameter estimates are known to be sensitive to such decisions, the claim that the package supplies 'thorough instructions' cannot be independently verified from the presented results.
  2. [Spatial modeling subsection] Section on spatial max-stable models: the paper does not state whether the reported parameter estimates include standard errors obtained from the full likelihood or from a composite-likelihood approximation, nor whether the spatial dependence range was estimated jointly or fixed a priori; this information is required to assess the reliability of the fitted surfaces shown in the figures.
minor comments (2)
  1. [Multivariate methods] Notation for the logistic model parameters is introduced without an explicit link to the corresponding function arguments in the ExtremalDep package; adding a short table mapping symbols to function names would improve usability.
  2. [Figures] Figure captions for the spatial dependence plots omit the coordinate system and the units of the distance axis; this makes it difficult to interpret the range of dependence.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and indicate planned revisions to improve reproducibility.

read point-by-point responses

  1. Referee: Applications section (real-world examples): the manuscript does not report the precise threshold-selection procedure or block-maxima definitions used for each dataset, nor does it include sensitivity checks on these choices; because extremal-dependence parameter estimates are known to be sensitive to such decisions, the claim that the package supplies 'thorough instructions' cannot be independently verified from the presented results.

    Authors: We agree that explicit documentation of threshold selection and block-maxima definitions is required for independent verification. The revised manuscript will add these details for each dataset together with sensitivity checks on the key modeling choices. revision: yes

  2. Referee: Section on spatial max-stable models: the paper does not state whether the reported parameter estimates include standard errors obtained from the full likelihood or from a composite-likelihood approximation, nor whether the spatial dependence range was estimated jointly or fixed a priori; this information is required to assess the reliability of the fitted surfaces shown in the figures.

    Authors: We acknowledge the omission. The revision will specify the likelihood method used for standard errors and clarify whether the spatial range was estimated jointly or held fixed. revision: yes

Circularity Check

0 steps flagged

Expository paper; no derivations or predictions present

full rationale

The manuscript is instructional: it supplies background on multivariate/spatial extremes and demonstrates the ExtremalDep R package via applications. No equations, fitted parameters, uniqueness theorems, or predictions are introduced that could reduce to self-defined inputs or self-citations. All content is external to any internal derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The paper rests on standard extreme value theory already present in the literature and on the correctness of the ExtremalDep implementation; no new free parameters, axioms, or invented entities are introduced by the authors.

pith-pipeline@v0.9.0 · 5642 in / 1051 out tokens · 43085 ms · 2026-05-23T07:15:27.426994+00:00 · methodology

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Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages · 1 internal anchor

  1. [1]

    Goegebeur, J

    Beirlant, J., Y. Goegebeur, J. Segers, and J. L. Teugels (2004). Statistics of extremes: theory and applications . John Wiley & Sons

    work page 2004

  2. [2]

    Belzile, L. R., C. Dutang, P. J. Northrop, and T. Opitz (2023). A modeler's guide to extreme value software. Extremes\/ 26\/ (4), 595--638

    work page 2023

  3. [3]

    Belzile, L. R., S. D. Grimshaw, R. Huser, P. J. Northrop, and J. L. Wadsworth (2022). mev: Modelling of Extreme Values . R package version 1.17

    work page 2022

  4. [4]

    Beranger, B. and S. A. Padoan (2015). Extreme dependence models. In Extreme Value Modeling and Risk Analysis , pp.\ 325--352. Chapman and Hall/CRC

    work page 2015

  5. [5]

    Beranger, B., S. A. Padoan, and G. Marcon (2025). ExtremalDep: Extremal Dependence Models . R package version 1.0.0

    work page 2025

  6. [6]

    Beranger, B., S. A. Padoan, and S. A. Sisson (2017). Models for extremal dependence derived from skew-symmetric families. Scandinavian Journal of Statistics\/ 44\/ (1), 21--45

    work page 2017

  7. [7]

    Beranger, B., S. A. Padoan, and S. A. Sisson (2021). Estimation and uncertainty quantification for extreme quantile regions. Extremes\/ 24\/ (2), 349--375

    work page 2021

  8. [8]

    Beranger, B., A. G. Stephenson, and S. A. Sisson (2021). High-dimensional inference using the extremal skew-t process. Extremes\/ 24\/ (3), 653--685

    work page 2021

  9. [9]

    Naveau, M

    Bernard, E., P. Naveau, M. Vrac, and O. Mestre (2013). Clustering of maxima: Spatial dependencies among heavy rainfall in france. Journal of climate\/ 26\/ (20), 7929--7937

    work page 2013

  10. [10]

    Brown, B. M. and S. I. Resnick (1977). Extreme values of independent stochastic processes. J. Appl. Probability\/ 14\/ (4), 732--739

    work page 1977

  11. [11]

    Cai, J.-J., J. H. Einmahl, and L. De Haan (2011). Estimation of extreme risk regions under multivariate regular variation. The Annals of Statistics\/ 39\/ (3), 1803--1826

    work page 2011

  12. [12]

    Coles, S. (2001). An introduction to statistical modeling of extreme values . Springer

    work page 2001

  13. [13]

    Coles, S. G. and J. A. Tawn (1991). Modelling extreme multivariate events. Journal of the Royal Statistical Society: Series B (Methodological)\/ 53\/ (2), 377--392

    work page 1991

  14. [14]

    Cooley, D., R. A. Davis, and P. Naveau (2010). The pairwise beta distribution: a flexible parametric multivariate model for extremes. J. Multivariate Anal.\/ 101\/ (9), 2103--2117

    work page 2010

  15. [15]

    Genest, and J

    Cormier, E., C. Genest, and J. G. Ne s lehov \'a (2014). Using b-splines for nonparametric inference on bivariate extreme-value copulas. Extremes\/ 17\/ (4), 633--659

    work page 2014

  16. [16]

    Davis, R. A., T. Mikosch, and I. Cribben (2011). Estimating extremal dependence in univariate and multivariate time series via the extremogram. https://arxiv.org/abs/1107.5592\/

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  17. [17]

    Davison, A. C., S. A. Padoan, and M. Ribatet (2012). Statistical modeling of spatial extremes, with discussion. Statistical Science\/ 27\/ (2), 161–186

    work page 2012

  18. [18]

    de Fondeville, R. and L. R. Belzile (2021). mvPot: Multivariate peaks-over-threshold modelling for spatial extreme events . R package version 0.1.5

    work page 2021

  19. [19]

    de Fondeville, R. and A. C. Davison (2018). High-dimensional peaks-over-threshold inference. Biometrika\/ 105\/ (3), 575–592

    work page 2018

  20. [20]

    de Haan, L. and A. Ferreira (2006). Extreme value theory: an introduction , Volume 21. Springer

    work page 2006

  21. [21]

    Engelke, and M

    Dombry, C., S. Engelke, and M. Oesting (2016). Exact simulation of max-stable processes. Biometrika\/ 103\/ (2), 303--317

    work page 2016

  22. [22]

    Einmahl, J. H., L. de Haan, and A. Krajina (2013). Estimating extreme bivariate quantile regions. Extremes\/ 16\/ (2), 121--145

    work page 2013

  23. [23]

    Engelke, S. and A. S. Hitz (2020). Graphical models for extremes. Journal of the Royal Statistical Society: Series B\/ 84\/ (4), 871–932

    work page 2020

  24. [24]

    Engelke, S., A. S. Hitz, N. Gnecco, and M. Hentschel (2024). graphicalExtremes: Statistical Methodology for Graphical Extreme Value Models . R package version 0.3.2

    work page 2024

  25. [25]

    Malinowski, Z

    Engelke, S., A. Malinowski, Z. Kabluchko, and M. Schlather (2015). Estimation of h \"u sler--reiss distributions and brown--resnick processes. Journal of the Royal Statistical Society: Series B (Statistical Methodology)\/ 77\/ (1), 239--265

    work page 2015

  26. [26]

    H \"u sler, and R.-D

    Falk, M., J. H \"u sler, and R.-D. Reiss (2010). Laws of small numbers: extremes and rare events . Springer Science & Business Media

    work page 2010

  27. [27]

    Guillou, and J

    Fils-Villetard, A., A. Guillou, and J. Segers (2008). Projection estimators of pickands dependence functions. Canadian Journal of Statistics\/ 36\/ (3), 369--382

    work page 2008

  28. [28]

    Frolova, N. and I. Cribben (2016). extremogram: Estimation of Extreme Value Dependence for Time Series Data . R package version 1.0.2

    work page 2016

  29. [29]

    Garthwaite, P. H., Y. Fan, and S. A. Sisson (2016). Adaptive optimal scaling of metropolis--hastings algorithms using the robbins--monro process. Communications in Statistics-Theory and Methods\/ 45\/ (17), 5098--5111

    work page 2016

  30. [30]

    Gilleland, E. and R. W. Katz (2016). extremes 2.0: A n extreme value analysis package in R . Journal of Statistical Software\/ 72\/ (8), 1--39

    work page 2016

  31. [31]

    Saksman, and J

    Haario, H., E. Saksman, and J. Tamminen (2001). An adaptive Metropolis algorithm. Bernoulli\/ 7 , 223--242

    work page 2001

  32. [32]

    He, Y. and J. H. Einmahl (2017). Estimation of extreme depth-based quantile regions. Journal of the Royal Statistical Society: Series B (Statistical Methodology)\/ 79\/ (2), 449--461

    work page 2017

  33. [33]

    Heffernan, J. E. and A. G. Stephenson (2018). ismev: An introduction to statistical modeling of extreme values . R package version 1.4.2

    work page 2018

  34. [34]

    Heffernan, J. E. and J. A. Tawn (2004). A conditional approach for multivariate extreme values (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology)\/ 66\/ (3), 497--546

    work page 2004

  35. [35]

    Hijmans, R. J. (2024). terra: Spatial Data Analysis . R package version 1.7-78

    work page 2024

  36. [36]

    Joe, H. (2014). Dependence modeling with copulas . CRC press

    work page 2014

  37. [37]

    Naveau, and S

    Marcon, G., P. Naveau, and S. Padoan (2017). A semi-parametric stochastic generator for bivariate extreme events. Stat\/ 6\/ (1), 184--201

    work page 2017

  38. [38]

    Marcon, G., S. A. Padoan, and I. Antoniano-Villalobos (2016). Bayesian inference for the extremal dependence. Electronic Journal of Statistics\/ 10\/ (2), 3310--3337

    work page 2016

  39. [39]

    Marcon, G., S. A. Padoan, P. Naveau, P. Muliere, and J. Segers (2017). Multivariate nonparametric estimation of the P ickands dependence function using B ernstein polynomials. J. Statist. Plann. Inference\/ 183 , 1--17

    work page 2017

  40. [40]

    Northrop, P. J. and N. Attalides (2016). Posterior propriety in bayesian extreme value analyses using reference priors. Statistica Sinica\/ 26\/ (2), 721--743

    work page 2016

  41. [41]

    Opitz, T. (2013). Extremal t processes: Elliptical domain of attraction and a spectral representation. Journal of Multivariate Analysis\/ 122\/ (0), 409 -- 413

    work page 2013

  42. [42]

    Padoan, S. A., M. Ribatet, and S. A. Sisson (2010). Likelihood-based inference for max-stable processes. Journal of the American Statistical Association\/ 105\/ (489), 263--277

    work page 2010

  43. [43]

    Padoan, S. A. and G. Stupfler (2020). ExtremeRisks: Extreme risk measures . R package version 0.0.4

    work page 2020

  44. [44]

    Ribatet, M. (2022). SpatialExtremes: Modelling Spatial Extremes . R package version 2.1-0

    work page 2022

  45. [45]

    Roberts, G. O., A. Gelman, and W. R. Gilks (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms. Annals of Applied Probability\/ 7\/ (1), 110--120

    work page 1997

  46. [46]

    Naveau, and A.-L

    Sabourin, A., P. Naveau, and A.-L. Fougeres (2013). Bayesian model averaging for multivariate extremes. Extremes\/ 16\/ (3), 325--350

    work page 2013

  47. [47]

    Stephenson, A. and J. Tawn (2005). Exploiting occurrence times in likelihood inference for componentwise maxima. Biometrika\/ 92\/ (1), 213--227

    work page 2005

  48. [48]

    Stephenson, A. G. (2002, June). evd: Extreme value distributions. R News\/ 2\/ (2), 31--32

    work page 2002

  49. [49]

    Stephenson, A. G. and M. Ribatet (2023). evdbayes: Bayesian Analysis in Extreme Value Theory . R package version 1.1-3

    work page 2023

  50. [50]

    Ypma, J. and S. G. Johnson (2022). The nlopt nonlinear-optimization package. R package version 2.0.3

    work page 2022