Pith. sign in

REVIEW 3 major objections 5 minor 162 references

The paper argues that spatial copula models are only coherent when their finite-location copulas satisfy Kolmogorov consistency—a condition that disqualifies many flexible constructions.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 03:42 UTC pith:HK5YL7KR

load-bearing objection A solid review that makes the finite-domain vs process-level distinction stick; the math is right, the literature-novelty claim is unverified but not fatal. the 3 major comments →

arxiv 2607.23063 v1 pith:HK5YL7KR submitted 2026-07-25 stat.ME

Copulas for Geostatistical Data: Foundations, Modeling Principles and Statistical Inference

Axel B\"ucher , Nadja Klein This is my paper
classification stat.ME MSC 62H0560G6062M30
keywords copula random fieldKolmogorov consistencySklar's theoremspatial dependencegeostatisticscopula semivariogramvine copulasimplicit copulas
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This review claims that copula modeling for geostatistical data hinges on a distinction most of the literature blurs: a copula specified for a fixed set of locations is not automatically part of a legitimate spatial random field. Any genuine field gives rise to a whole family of finite-dimensional copulas, and that family must obey permutation and marginal consistency under Kolmogorov's extension theorem. The authors show that flexible fixed-dimensional tools such as vine copulas therefore fail as process-level models unless explicitly checked, while 'implicit' constructions—taking a known random field and standardizing its margins—always yield valid fields. They also introduce copula-based semivariograms that expose tail behavior and asymmetry invisible to classical variograms, and they survey inference and prediction once a valid field is in hand. If the review's framing is right, it supplies a common criterion for judging all spatial copula models and clarifies why the existing repertoire of process-level copula fields remains small.

Core claim

On the paper's own terms, the central discovery is that Sklar's theorem lifts from vectors to random fields only through consistency: a spatial copula model on an infinite domain is nothing but a family of copulas indexed by finite location sets, and such a family defines a bona fide copula random field exactly when it satisfies permutation invariance and marginal consistency. Any construction obtained by marginal standardization of an existing random field (Gaussian, t, max-stable, gamma-based) automatically satisfies these conditions; bottom-up constructions such as pairwise or vine copulas generally do not. The review systematizes this split between finite-domain models and process-level

What carries the argument

The Kolmogorov consistency conditions (permutation invariance and marginal consistency) for a family of copula finite-dimensional distributions; and the 'implicit copula field' construction, which obtains a copula random field by standardizing the margins of a known random field. The family of lag-indexed bivariate copulas C_h under strict bivariate stationarity carries the dependence diagnostics, including the copula semivariogram γ_{C,u}(h) = u − C_h(u,u).

Load-bearing premise

The paper's originality claim rests on its assertion that no existing review systematically connects copula theory, random-field consistency, and spatial statistics; if such a review already exists, the central contribution is void. The modeling framework also assumes strict bivariate stationarity and continuous margins, without which the lag-indexed copula is no longer well defined.

What would settle it

Finding a published systematic review that already covers this same unification would directly undercut the novelty claim. For the technical claim, a concrete falsifier is a finite-location copula family that satisfies neither permutation nor marginal consistency yet produces sensible bivariate fits—demonstrating that without the consistency check, such a family can masquerade as a spatial model.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Any practical spatial copula model must be testable against the two consistency conditions before being used for simulation or prediction.
  • Vine and other fixed-dimensional copula constructions should be treated as finite-domain approximations, not as full random fields, unless a consistency proof is supplied.
  • Implicit constructions—Gaussian copula fields, chi-square/Fisher copula fields, factor copula fields, Clayton-like fields—provide a ready-made menu of valid process-level models.
  • Copula semivariograms give diagnostics for tail dependence and radial asymmetry that second-order variograms cannot detect.
  • The conditional-copula prediction formula turns any valid copula field into a full predictive distribution for unobserved locations under plug-in estimates.

Where Pith is reading between the lines

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

  • A concrete testable extension is a screening procedure: for a candidate pairwise copula family, check numerically whether the implied d-dimensional copulas satisfy marginal consistency; failures would show up as discrepancies in low-dimensional margins.
  • The consistency framing suggests a design principle for new spatial copula models: start from a latent process and define the copula field by transformation, rather than trying to patch fixed-dimensional copulas together.
  • The same Kolmogorov lens could be applied to spatio-temporal copula constructions, where the paper notes systematic study is still missing, and to covariate-indexed copula families, where compatibility is easy to violate.
  • If taken up, the review's taxonomy could underpin software validators that check Kolmogorov consistency before a copula model is accepted for kriging-style prediction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This review paper brings together copula theory and geostatistical modeling. Its central thesis is that a spatial copula model is not just a family of finite-dimensional copulas but must satisfy Kolmogorov consistency conditions to define a genuine random field on a continuous spatial domain. The paper revisits classical geostatistical tools through a copula lens (Sections 3.1–3.3), reviews process-level constructions such as implicit copula fields, factor copula fields, and Archimedean/Clayton random fields (Sections 4.2–4.3), discusses finite-domain vine copula models (Section 4.3), covariate incorporation (Section 4.4), statistical inference and prediction (Section 5), spatio-temporal extensions (Section 6), and closes with open problems (Section 7). The distinction between finite-domain models and process-level constructions is developed carefully and is supported by correct derivations of the indicator-variogram identity and the copula cross-semivariogram expansion.

Significance. If the synthesis holds, the paper provides a useful conceptual unification: it clarifies that arbitrary collections of copulas indexed by finite location sets do not automatically define a spatial random field, and it organizes a dispersed literature around that distinction. The paper's strengths include its explicit treatment of Kolmogorov consistency (Section 4.1), its correction of Bárdossy's indicator-variogram formula (Section 3.1), its candid discussion of the limited asymptotic theory for single-realization spatial copula inference (Section 5.1), and its broad coverage of spatio-temporal extensions and software (Sections 5.3 and 6). The paper is honest about open questions, which is a genuine strength for a review. Its value as an original contribution rests primarily on the claim in Section 1 that no existing review systematically covers these strands; that claim needs substantiation.

major comments (3)
  1. [Section 1] The statement 'To the best of our knowledge, no existing review systematically brings these strands together' is load-bearing for the paper's status as a review, but it is not supported by any systematic literature search, inclusion criteria, or explicit comparison with the closest existing surveys (e.g., reviews of spatial extremes, implicit copulas, or vine copulas). If a prior review already covers the same finite-domain/process-level distinction, the contribution is significantly reduced. Please document the search and compare with the closest works, or substantially weaken the novelty claim by delineating precisely what is new relative to those works.
  2. [Section 4 and Section 5.3] The definition of copula fidis in Section 4 relies on Sklar's theorem without qualification about continuity of margins. For discrete margins the copula is not unique, so 'the' copula fidis are not well-defined and the finite-domain/process-level dichotomy becomes ambiguous. Since the paper explicitly mentions count data and geostatistical count models (Section 2.2.4 and Section 5.3 via gcKrig), this is not an irrelevant edge case. Please state the continuous-margin assumption prominently and explain how the framework is affected for discrete margins, e.g., non-identifiability and the need for additional conventions.
  3. [Section 4.4] The statement that 'any copula-field construction in which pairwise dependence can be parameterized through a, not necessarily Euclidean, distance on the underlying domain remains valid after this embedding' is overly broad. For Gaussian-copula fields with an isotropic correlation function, validity on R^2 does not automatically imply validity on R^q for q>2; positive definiteness must hold on the specific metric space and dimension. Please qualify this claim or restrict it to constructions whose validity is known to be preserved under the augmented distance.
minor comments (5)
  1. [Section 3.1] When stating that γ^C_{1/2}(h)=(1−β_h)/4, please define β_h explicitly as β_h=4C_h(1/2,1/2)−1 to avoid ambiguity about the convention for Blomqvist's beta.
  2. [Section 4.2.3] The notation G_2 and G_{2a} for the Gamma random fields is undefined as written. The standard Clayton representation uses E_i exponential and M_a∼Gamma(1/a,1). Please specify the shape/scale parameters of G_2 and G_{2a} so that the claimed marginal uniformity of U(s) and the bivariate copula formula can be verified.
  3. [Section 6.1.3] The factor process is written as V_t(s)=α(s,t)EP(t). The notation 'EP(t)' is unclear; please clarify whether E denotes an exponential variable and P(t) is an inhomogeneous Poisson process, and correct the typesetting.
  4. [Section 4.4] Typo: 'appraoch' should be 'approach'.
  5. [Section 5.3] The sentence about limited software support for spatial factor-copula models would benefit from a more concrete description of what is missing (e.g., scalable estimation, prediction intervals, or replicated-data handling).

Circularity Check

0 steps flagged

No significant circularity: the central Kolmogorov-consistency argument rests on an external theorem (Billingsley), the copula-semivariogram identities are derived from definitions, and the self-citations are contextual examples rather than load-bearing premises.

full rationale

The paper's central claim — that a family of copulas indexed by finite location sets defines a bona fide copula random field only if it satisfies permutation and marginal consistency — is an application of Kolmogorov's extension theorem, cited to Billingsley (1995), an external mathematical source that does not depend on the authors' own work. The copula-semivariogram formulas in Section 3.1 are derived step-by-step from the definition of the indicator semivariogram (e.g., gamma_beta(h) = F_Y(beta) - C_h(F_Y(beta), F_Y(beta)) follows from E[1(A<=beta)] - E[1(A<=beta)1(B<=beta)]), and the claimed correction to Bárdossy (2006, Eq. 10) is an externally checkable statement about a published formula, not a self-referential input. No parameter is fitted to data and then relabeled as a prediction; the only calibration in the paper is the illustrative choice in Figure 1 equating Spearman semivariograms across copulas, which is explicitly a display device. The self-citations (Bücher & Volgushev 2013; Klein & Kneib 2016; Smith & Klein 2021; Kock & Klein 2025; Riebl, Klein & Kneib 2023; Bach & Klein 2025; Labanca, Gotthard & Klein 2026) appear as examples of existing distributional-regression or copula methodology and as handles for further reading; none is invoked as the premise of the review's argument, and no uniqueness theorem from the authors' prior work is imported to force a modeling choice. The Section 1 literature claim ('To the best of our knowledge, no existing review systematically brings these strands together') is unverifiable from the text and is an originality risk, not a circularity per the rubric: it does not reduce any derivation to its inputs. The manuscript also candidly flags its own gaps (asymptotic theory for spatial copula estimators 'has not yet been studied'; broadly applicable inference theory 'remains limited'), which is consistent with a review that derives its content from external sources rather than from its own conclusions.

Axiom & Free-Parameter Ledger

0 free parameters · 5 axioms · 0 invented entities

No free parameters: the paper fits no data; the Figure 1 copula parameters are chosen only to illustrate a fixed Spearman semivariogram and do not enter the central claims. No invented entities: the review introduces no new latent variables, forces, or quantities; the objects it discusses (copula fidis, factor copula fields, the copula semivariogram) are either from the literature or are functions of existing copulas. The load-bearing mathematics is standard (Sklar, Kolmogorov); domain assumptions (continuity, stationarity, ergodicity) are explicit in the text.

axioms (5)
  • standard math Sklar's theorem: every d-dimensional cdf factors as C(F_1,...,F_d); copula is unique when margins are continuous.
    Theorem 1, Section 2.2.1; foundation for defining copula fidis of a random field.
  • standard math Kolmogorov's extension theorem: consistent finite-dimensional distributions (permutation + marginal consistency) define a stochastic process on the index set.
    Section 4.1; used to state necessary and sufficient conditions for a family of copulas to form a copula random field.
  • domain assumption Existence of Gaussian, Student-t, Gamma, and max-stable random fields with prescribed covariance/correlation functions.
    Section 4.2; implicit copula-field constructions start from these fields; existence is imported from the cited literature.
  • domain assumption Continuous marginal cdfs for the unique copula fidis; strict bivariate stationarity for lag-indexed copulas.
    Sections 3 and 4; the paper flags that non-continuous margins make the copula non-unique.
  • domain assumption Ergodicity or mixing conditions justify pooling across spatial lags in single-realization inference.
    Section 5.1; the paper notes these conditions are required and that general theory remains open.

pith-pipeline@v1.3.0-alltime-deepseek · 31934 in / 21978 out tokens · 201457 ms · 2026-08-01T03:42:37.436182+00:00 · methodology

0 comments
read the original abstract

Spatial statistics commonly describes spatial dependence through second-order quantities such as covariance functions and variograms, often within Gaussian random-field models and under structural assumptions such as stationarity, isotropy, or distance-based decay. Copulas offer a complementary framework that separates marginal distributions from dependence and permits a broad range of non-Gaussian dependence structures. Because the finite-dimensional distributions of a spatial random field can always be decomposed into margins and copulas through Sklar's theorem, copulas provide a natural language for studying spatial dependence beyond second-order summaries. Yet the relevant literature has developed along several largely separate strands across spatial statistics, copula modeling, stochastic processes, and application domains, often with different terminology and modeling objectives. This review brings these strands together: We revisit classical concepts from spatial statistics through a copula lens, discuss copula-based tools for describing spatial dependence, and systematically review constructions of spatial copula models. Particular emphasis is placed on Kolmogorov consistency and on the distinction between models defined for a fixed set of locations and genuinely process-level constructions. We also discuss statistical inference, extensions to spatio-temporal settings, and emerging directions involving flexible marginal and dependence models. By clarifying the relationships among existing approaches and their respective strengths and limitations, the review provides a unified perspective on the interface between copula modeling and spatial statistics.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

162 extracted references · 70 canonical work pages

  1. [1]

    , TITLE =

    Sang, Huiyan and Gelfand, Alan E. , TITLE =. J. Agric. Biol. Environ. Stat. , FJOURNAL =. 2010 , NUMBER =. doi:10.1007/s13253-009-0010-1 , URL =

    work page doi:10.1007/s13253-009-0010-1 2010

  2. [2]

    Electron

    Masarotto, Guido and Varin, Cristiano , TITLE =. Electron. J. Stat. , FJOURNAL =. 2012 , PAGES =. doi:10.1214/12-EJS721 , URL =

    work page doi:10.1214/12-ejs721 2012

  3. [3]

    , TITLE =

    Ribatet, Mathieu and Cooley, Daniel and Davison, Anthony C. , TITLE =. Statist. Sinica , FJOURNAL =. 2012 , NUMBER =

    2012

  4. [4]

    Bevilacqua, Moreno and Gaetan, Carlo , TITLE =. Stat. Comput. , FJOURNAL =. 2015 , NUMBER =. doi:10.1007/s11222-014-9460-6 , URL =

    doi:10.1007/s11222-014-9460-6 2015

  5. [5]

    , TITLE =

    Bai, Yun and Kang, Jian and Song, Peter X.-K. , TITLE =. Biometrics , FJOURNAL =. 2014 , NUMBER =. doi:10.1111/biom.12199 , URL =

    work page doi:10.1111/biom.12199 2014

  6. [6]

    , title =

    Joe, Harry and Xu, James J. , title =

  7. [7]

    B\"ucher, Axel and Volgushev, Stanislav , TITLE =. J. Multivariate Anal. , FJOURNAL =. 2013 , PAGES =. doi:10.1016/j.jmva.2013.04.003 , URL =

    work page doi:10.1016/j.jmva.2013.04.003 2013

  8. [8]

    W. R. Tobler , journal =. A Computer Movie Simulating Urban Growth in the Detroit Region , urldate =

  9. [9]

    and Nagler, T

    Meyer, D. and Nagler, T. and Hogan, R. J. , TITLE =. Geoscientific Model Development , VOLUME =. 2021 , NUMBER =

    2021

  10. [10]

    2021 , journal =

    Copula Flows for Synthetic Data Generation , author=. 2021 , journal =. 2101.00598 , archivePrefix=

    Pith/arXiv arXiv 2021

  11. [11]

    Copulas as High-Dimensional Generative Models: Vine Copula Autoencoders , url =

    Tagasovska, Natasa and Ackerer, Damien and Vatter, Thibault , booktitle =. Copulas as High-Dimensional Generative Models: Vine Copula Autoencoders , url =

  12. [12]

    and Calder, Catherine A

    Risser, Mark D. and Calder, Catherine A. , TITLE =. Environmetrics , FJOURNAL =. 2015 , NUMBER =. doi:10.1002/env.2336 , URL =

    work page doi:10.1002/env.2336 2015

  13. [13]

    arXiv preprint arXiv:2603.21075 , year =

    Fynn, Daniel and Gunawan, David and Zammit-Mangion, Andrew , title =. arXiv preprint arXiv:2603.21075 , year =

    arXiv

  14. [14]

    arXiv preprint arXiv:2601.01813 , year =

    Nag, Pratik and Zammit-Mangion, Andrew and Singh, Sumeetpal and Cressie, Noel , title =. arXiv preprint arXiv:2601.01813 , year =

    arXiv

  15. [16]

    Sainsbury-Dale, Matthew and Zammit-Mangion, Andrew and Huser, Rapha\"el , TITLE =. Amer. Statist. , FJOURNAL =. 2024 , NUMBER =. doi:10.1080/00031305.2023.2249522 , URL =

    Pith/arXiv arXiv 2024

  16. [17]

    Neural Conditional Simulation for Complex Spatial Processes , journal =

    Walchessen, Julia and Zammit-Mangion, Andrew and Huser, Rapha. Neural Conditional Simulation for Complex Spatial Processes , journal =

  17. [18]

    arXiv preprint arXiv:2509.12884 , year =

    Nag, Pratik and Zammit-Mangion, Andrew and Sun, Ying , title =. arXiv preprint arXiv:2509.12884 , year =

    Pith/arXiv arXiv

  18. [19]

    Coblenz, Maximilian and Grothe, Oliver and Liu, Bolin and Weniger, David , TITLE =. Depend. Model. , FJOURNAL =. 2026 , NUMBER =. doi:10.1515/demo-2025-0017 , URL =

    work page doi:10.1515/demo-2025-0017 2026

  19. [20]

    and Eidsvik, Jo and Guindani, Michele and Nail, Amy J

    Reich, Brian J. and Eidsvik, Jo and Guindani, Michele and Nail, Amy J. and Schmidt, Alexandra M. , TITLE =. Ann. Appl. Stat. , FJOURNAL =. 2011 , NUMBER =. doi:10.1214/11-AOAS482 , URL =

    doi:10.1214/11-aoas482 2011

  20. [21]

    and Guttorp, Peter and O'Hagan, Anthony , TITLE =

    Schmidt, Alexandra M. and Guttorp, Peter and O'Hagan, Anthony , TITLE =. Environmetrics , FJOURNAL =. 2011 , NUMBER =. doi:10.1002/env.1101 , URL =

    doi:10.1002/env.1101 2011

  21. [22]

    2016 , eprint=

    Review: Nonstationary Spatial Modeling, with Emphasis on Process Convolution and Covariate-Driven Approaches , author=. 2016 , eprint=

    2016

  22. [23]

    Bayesian Anal

    Grazian, Clara and Liseo, Brunero , TITLE =. Bayesian Anal. , FJOURNAL =. 2017 , NUMBER =. doi:10.1214/17-BA1080 , URL =

    work page doi:10.1214/17-ba1080 2017

  23. [24]

    2012 , PAGES =

    Mai, Jan-Frederik and Scherer, Matthias , TITLE =. 2012 , PAGES =. doi:10.1142/p842 , URL =

    work page doi:10.1142/p842 2012

  24. [26]

    M\"uller, Dominik and Czado, Claudia , TITLE =. Stat. Comput. , FJOURNAL =. 2019 , NUMBER =. doi:10.1007/s11222-018-9807-5 , URL =

    work page doi:10.1007/s11222-018-9807-5 2019

  25. [27]

    Liu, Han and Han, Fang and Yuan, Ming and Lafferty, John and Wasserman, Larry , TITLE =. Ann. Statist. , FJOURNAL =. 2012 , NUMBER =. doi:10.1214/12-AOS1037 , URL =

    work page doi:10.1214/12-aos1037 2012

  26. [28]

    Padoan, S. A. and Ribatet, M. and Sisson, S. A. , TITLE =. J. Amer. Statist. Assoc. , FJOURNAL =. 2010 , NUMBER =. doi:10.1198/jasa.2009.tm08577 , URL =

    work page doi:10.1198/jasa.2009.tm08577 2010

  27. [29]

    Varin, Cristiano and Reid, Nancy and Firth, David , TITLE =. Statist. Sinica , FJOURNAL =. 2011 , NUMBER =

    2011

  28. [30]

    Copula modelling of dependence in multivariate time series , journal =

    Michael Stanley Smith , keywords =. Copula modelling of dependence in multivariate time series , journal =. 2015 , issn =. doi:https://doi.org/10.1016/j.ijforecast.2014.04.003 , url =

    work page doi:10.1016/j.ijforecast.2014.04.003 2015

  29. [31]

    Klein, Nadja , TITLE =. Annu. Rev. Stat. Appl. , FJOURNAL =. 2024 , PAGES =. doi:10.1146/annurev-statistics-040722-053607 , URL =

    doi:10.1146/annurev-statistics-040722-053607 2024

  30. [32]

    and Seo, Juwon , TITLE =

    Beare, Brendan K. and Seo, Juwon , TITLE =. J. Time Series Anal. , FJOURNAL =. 2015 , NUMBER =. doi:10.1111/jtsa.12103 , URL =

    work page doi:10.1111/jtsa.12103 2015

  31. [33]

    Nagler, Thomas and Kr\"uger, Daniel and Min, Aleksey , TITLE =. J. Econometrics , FJOURNAL =. 2022 , NUMBER =. doi:10.1016/j.jeconom.2021.11.015 , URL =

    work page doi:10.1016/j.jeconom.2021.11.015 2022

  32. [34]

    Spatiotemporal modeling of wind generation for optimal energy storage sizing , year=

    Haghi, Hamed Valizadeh and Lotfifard, Saeed , booktitle=. Spatiotemporal modeling of wind generation for optimal energy storage sizing , year=

  33. [35]

    How well do regional climate models simulate the spatial dependence of precipitation? An application of pair-copula constructions , journal =

    Hob. How well do regional climate models simulate the spatial dependence of precipitation? An application of pair-copula constructions , journal =. 2015 , pages =. doi:https://doi.org/10.1002/2014JD022748 , url =

    work page doi:10.1002/2014jd022748 2015

  34. [36]

    Selecting and estimating regular vine copulae and application to financial returns , JOURNAL =

    Di. Selecting and estimating regular vine copulae and application to financial returns , JOURNAL =. 2013 , PAGES =. doi:10.1016/j.csda.2012.08.010 , URL =

    work page doi:10.1016/j.csda.2012.08.010 2013

  35. [37]

    and Varshney, Pramod K

    Philippe, Wolf Peter Jean and Zhang, Shan and Eftekharnejad, Sara and Ghosh, Prasanta K. and Varshney, Pramod K. , journal=. Mixed Copula-Based Uncertainty Modeling of Hourly Wind Farm Production for Power System Operational Planning Studies , year=

  36. [38]

    Lee and Jiale Xie and Yupeng Jin , keywords =

    Yu Huang and Bingzhe Zhang and Huizhen Pang and Biao Wang and Kwang Y. Lee and Jiale Xie and Yupeng Jin , keywords =. Spatio-temporal wind speed prediction based on Clayton Copula function with deep learning fusion , journal =. 2022 , issn =. doi:https://doi.org/10.1016/j.renene.2022.04.055 , url =

    work page doi:10.1016/j.renene.2022.04.055 2022

  37. [39]

    2025 , issn =

    Modelling time series with temporal and spatial correlations in transport planning using hierarchical ARIMA-copula Model: A Bayesian approach , journal =. 2025 , issn =. doi:https://doi.org/10.1016/j.eswa.2025.126977 , url =

    arXiv 2025

  38. [40]

    A periodic spatial vine copula model for multi-site streamflow simulation , journal =

    Pereira, Guilherme and Veiga, \'. A periodic spatial vine copula model for multi-site streamflow simulation , journal =. 2017 , issn =. doi:https://doi.org/10.1016/j.epsr.2017.06.017 , url =

    work page doi:10.1016/j.epsr.2017.06.017 2017

  39. [41]

    2016 Power Systems Computation Conference (PSCC) , title=

    Pereira, Guilherme and Veiga, \'. 2016 Power Systems Computation Conference (PSCC) , title=. 2016 , volume=

    2016

  40. [42]

    , TITLE =

    Sohrabian, B. , TITLE =. Spat. Stat. , FJOURNAL =. 2021 , PAGES =. doi:10.1016/j.spasta.2020.100488 , URL =

    arXiv 2021

  41. [43]

    and Nguyen, Bao and Olsen, Elwood T

    Darsow, William F. and Nguyen, Bao and Olsen, Elwood T. , TITLE =. Illinois J. Math. , FJOURNAL =. 1992 , NUMBER =

    1992

  42. [44]

    Chen, Xiaohong and Fan, Yanqin , TITLE =. J. Econometrics , FJOURNAL =. 2006 , NUMBER =. doi:10.1016/j.jeconom.2005.03.004 , URL =

    work page doi:10.1016/j.jeconom.2005.03.004 2006

  43. [45]

    Dell'Oro, Lorenzo and Gaetan, Carlo , TITLE =. Spat. Stat. , FJOURNAL =. 2025 , PAGES =. doi:10.1016/j.spasta.2025.100916 , URL =

    arXiv 2025

  44. [46]

    , TITLE =

    Cressie, Noel and Wikle, Christopher K. , TITLE =. 2011 , PAGES =

    2011

  45. [47]

    and Zammit-Mangion, Andrew and Cressie, Noel , TITLE =

    Wikle, Christopher K. and Zammit-Mangion, Andrew and Cressie, Noel , TITLE =. 2019 , PAGES =

    2019

  46. [48]

    2026 , note =

    copula: Multivariate Dependence with Copulas , author =. 2026 , note =

    2026

  47. [49]

    2026 , note =

    GeoModels: Procedures for Gaussian and Non Gaussian Geostatistical (Large) Data Analysis , author =. 2026 , note =

    2026

  48. [50]

    Okhrin, Ostap and Okhrin, Yarema and Schmid, Wolfgang , TITLE =. J. Econometrics , FJOURNAL =. 2013 , NUMBER =. doi:10.1016/j.jeconom.2012.12.001 , URL =

    work page doi:10.1016/j.jeconom.2012.12.001 2013

  49. [51]

    2025 , note =

    VineCopula: Statistical Inference of Vine Copulas , author =. 2025 , note =

    2025

  50. [52]

    , title =

    Juang, Kai-Wei and Lee, Dar-Yuan and Ellsworth, Timothy R. , title =. Journal of Environmental Quality , volume =. doi:https://doi.org/10.2134/jeq2001.303894x , url =. https://acsess.onlinelibrary.wiley.com/doi/pdf/10.2134/jeq2001.303894x , year =

    arXiv

  51. [53]

    and Nott, David J

    Klein, Nadja and Smith, Michael Stanley and Chisholm, Ryan A. and Nott, David J. , TITLE =. J. Comput. Graph. Statist. , FJOURNAL =. 2025 , NUMBER =. doi:10.1080/10618600.2025.2458504 , URL =

    arXiv 2025

  52. [54]

    Smith, Michael Stanley and Klein, Nadja , TITLE =. J. Bus. Econom. Statist. , FJOURNAL =. 2021 , NUMBER =. doi:10.1080/07350015.2020.1721295 , URL =

    arXiv 2021

  53. [55]

    , TITLE =

    Agarwal, Gaurav and Sun, Ying and Wang, Huixia J. , TITLE =. Spat. Stat. , FJOURNAL =. 2021 , PAGES =. doi:10.1016/j.spasta.2021.100524 , URL =

    arXiv 2021

  54. [56]

    Musgrove, D. R. and Hughes, J. and Eberly, L. E. , TITLE =. Spat. Stat. , FJOURNAL =. 2016 , PAGES =. doi:10.1016/j.spasta.2016.04.006 , URL =

    work page doi:10.1016/j.spasta.2016.04.006 2016

  55. [57]

    and Schliep, Erin M

    Gelfand, Alan E. and Schliep, Erin M. , TITLE =. Spat. Stat. , FJOURNAL =. 2016 , PAGES =. doi:10.1016/j.spasta.2016.03.006 , URL =

    work page doi:10.1016/j.spasta.2016.03.006 2016

  56. [58]

    2024 , note =

    Pareto processes for threshold exceedances in spatial extremes , author=. 2024 , note =. 2407.05699 , archivePrefix=

    Pith/arXiv arXiv 2024

  57. [59]

    2025 , journal =

    Bayesian copula-based spatial random effects models for inference with complex spatial data , author=. 2025 , journal =. 2511.02551 , archivePrefix=

    arXiv 2025

  58. [60]

    Bernoulli , FJOURNAL =

    Ferreira, Ana and de Haan, Laurens , TITLE =. Bernoulli , FJOURNAL =. 2014 , NUMBER =. doi:10.3150/13-BEJ538 , URL =

    work page doi:10.3150/13-bej538 2014

  59. [61]

    , TITLE =

    Krupskii, Pavel and Genton, Marc G. , TITLE =. Spat. Stat. , FJOURNAL =. 2017 , PAGES =. doi:10.1016/j.spasta.2017.10.001 , URL =

    work page doi:10.1016/j.spasta.2017.10.001 2017

  60. [62]

    Castro-Camilo, Daniela and Huser, Rapha\"el , TITLE =. J. Amer. Statist. Assoc. , FJOURNAL =. 2020 , NUMBER =. doi:10.1080/01621459.2019.1647842 , URL =

    arXiv 2020

  61. [63]

    and Zhang, Hao , TITLE =

    Genton, Marc G. and Zhang, Hao , TITLE =. Chil. J. Stat. , FJOURNAL =. 2012 , NUMBER =

    2012

  62. [64]

    , TITLE =

    Nasri, Bouchra R. , TITLE =. Statist. Probab. Lett. , FJOURNAL =. 2020 , PAGES =. doi:10.1016/j.spl.2020.108704 , URL =

    arXiv 2020

  63. [65]

    Environmetrics , FJOURNAL =

    Favre, Anne-Catherine and Quessy, Jean-Fran cois and Toupin, Marie-H\'el\`ene , TITLE =. Environmetrics , FJOURNAL =. 2018 , NUMBER =. doi:10.1002/env.2494 , URL =

    work page doi:10.1002/env.2494 2018

  64. [66]

    , TITLE =

    Oh, Dong Hwan and Patton, Andrew J. , TITLE =. J. Bus. Econom. Statist. , FJOURNAL =. 2017 , NUMBER =. doi:10.1080/07350015.2015.1062384 , URL =

    arXiv 2017

  65. [67]

    Krupskii, Pavel and Joe, Harry , TITLE =. J. Multivariate Anal. , FJOURNAL =. 2013 , PAGES =. doi:10.1016/j.jmva.2013.05.001 , URL =

    work page doi:10.1016/j.jmva.2013.05.001 2013

  66. [68]

    and Straumann, Daniel , TITLE =

    Embrechts, Paul and McNeil, Alexander J. and Straumann, Daniel , TITLE =. Risk management: value at risk and beyond (. 2002 , ISBN =. doi:10.1017/CBO9780511615337.008 , URL =

    doi:10.1017/cbo9780511615337.008 2002

  67. [70]

    2019 , PAGES =

    Czado, Claudia , TITLE =. 2019 , PAGES =. doi:10.1007/978-3-030-13785-4 , URL =

    work page doi:10.1007/978-3-030-13785-4 2019

  68. [71]

    2015 , PAGES =

    Joe, Harry , TITLE =. 2015 , PAGES =

    2015

  69. [72]

    Czado, Claudia and Nagler, Thomas , TITLE =. Annu. Rev. Stat. Appl. , FJOURNAL =. 2022 , PAGES =. doi:10.1146/annurev-statistics-040220-101153 , URL =

    work page doi:10.1146/annurev-statistics-040220-101153 2022

  70. [73]

    , TITLE =

    Patton, Andrew J. , TITLE =. J. Multivariate Anal. , FJOURNAL =. 2012 , PAGES =. doi:10.1016/j.jmva.2012.02.021 , URL =

    doi:10.1016/j.jmva.2012.02.021 2012

  71. [74]

    and Ghoudi, K

    Genest, C. and Ghoudi, K. and Rivest, L.-P. , TITLE =. Biometrika , FJOURNAL =. 1995 , NUMBER =. doi:10.1093/biomet/82.3.543 , URL =

    work page doi:10.1093/biomet/82.3.543 1995

  72. [75]

    Biometrics , FJOURNAL =

    Erhardt, Tobias Michael and Czado, Claudia and Schepsmeier, Ulf , TITLE =. Biometrics , FJOURNAL =. 2015 , NUMBER =. doi:10.1111/biom.12279 , URL =

    work page doi:10.1111/biom.12279 2015

  73. [76]

    Genest, Christian and Segers, Johan , TITLE =. J. Multivariate Anal. , FJOURNAL =. 2010 , NUMBER =. doi:10.1016/j.jmva.2010.03.018 , URL =

    work page doi:10.1016/j.jmva.2010.03.018 2010

  74. [77]

    Krupskii, Pavel and Joe, Harry , TITLE =. J. Appl. Stat. , FJOURNAL =. 2015 , NUMBER =. doi:10.1080/02664763.2014.980787 , URL =

    arXiv 2015

  75. [78]

    and Sun, Ying and Hering, Amanda S

    Tang, Yanlin and Wang, Huixia J. and Sun, Ying and Hering, Amanda S. , TITLE =. Biometrics , FJOURNAL =. 2019 , NUMBER =. doi:10.1111/biom.13066 , URL =

    work page doi:10.1111/biom.13066 2019

  76. [79]

    Modelling Dependence in Space and Time with Vine Copulas , booktitle =

    Gr. Modelling Dependence in Space and Time with Vine Copulas , booktitle =. 2012 , note =

    2012

  77. [80]

    Smith, Michael and Min, Aleksey and Almeida, Carlos and Czado, Claudia , TITLE =. J. Amer. Statist. Assoc. , FJOURNAL =. 2010 , NUMBER =. doi:10.1198/jasa.2010.tm09572 , URL =

    work page doi:10.1198/jasa.2010.tm09572 2010

  78. [81]

    , TITLE =

    Huser, Rapha\"el and Wadsworth, Jennifer L. , TITLE =. Wiley Interdiscip. Rev. Comput. Stat. , FJOURNAL =. 2022 , NUMBER =. doi:10.1002/wics.1537 , URL =

    work page doi:10.1002/wics.1537 2022

  79. [82]

    Copula-based geostatistical modeling of continuous and discrete data including covariates , url =

    Kazianka, Hannes and Pilz, J. Copula-based geostatistical modeling of continuous and discrete data including covariates , url =. Stochastic Environmental Research and Risk Assessment , number =. doi:10.1007/s00477-009-0353-8 , isbn =

    doi:10.1007/s00477-009-0353-8

  80. [83]

    usler, J\

    H\"usler, J\"urg and Reiss, Rolf-Dieter , TITLE =. Statist. Probab. Lett. , FJOURNAL =. 1989 , NUMBER =. doi:10.1016/0167-7152(89)90106-5 , URL =

    work page doi:10.1016/0167-7152(89)90106-5 1989

Showing first 80 references.