588
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Vecchia Likelihood Approximation for Accurate and Fast Inference with Intractable Spatial Max-Stable Models

ORCID Icon, &
Received 11 Oct 2022, Accepted 14 Nov 2023, Published online: 28 Dec 2023

References

  • Beranger, B., Stephenson, A. G., and Sisson, S. A. (2021), “High-Dimensional Inference Using the Extremal Skew-t Process,” Extremes, 24, 653–685. DOI: 10.1007/s10687-020-00376-1.
  • Bopp, G., Shaby, B. A., and Huser, R. (2021), “A Hierarchical Max-Infinitely Divisible Spatial Model for Extreme Precipitation,” Journal of American Statistical Association, 116, 93–106. DOI: 10.1080/01621459.2020.1750414.
  • Bulgin, C. E., Merchant, C. J., and Ferreira, D. (2020), “Tendencies, Variability and Persistence of Sea Surface Temperature Anomalies,” Scientific Reports, 10, 7986. DOI: 10.1038/s41598-020-64785-9.
  • de Carvalho, M., and Davison, A. C. (2014), “Spectral Density Ratio Models for Multivariate Extremes,” Journal of the American Statistical Association, 109, 764–776. DOI: 10.1080/01621459.2013.872651.
  • Castruccio, S., Huser, R., and Genton, M. G. (2016), “High-Order Composite Likelihood Inference for Max-Stable Distributions and Processes,” Journal of Computational and Graphical Statistics, 25, 1212–129. DOI: 10.1080/10618600.2015.1086656.
  • Davis, R. A., Küppelberg, C., and Steinkohl, C. (2013), “Max-Stable Processes for Modeling Extremes Observed in Space and Time,” Journal of the Korean Statistical Society, 42, 399–414. DOI: 10.1016/j.jkss.2013.01.002.
  • Davison, A. C., and Huser, R. (2015), “Statistics of Extremes,” Annual Review of Statistics and its Application, 2, 203–235. DOI: 10.1146/annurev-statistics-010814-020133.
  • Davison, A. C., Huser, R., and Thibaud, E. (2019), “Spatial Extremes,” in: Handbook of Environmental and Ecological Statistics, eds. A. E. Gelfand, M. Fuentes, J. A. Hoeting, and R. L. Smith, pp. 711–744, Boca Raton, FL: CRC Press.
  • Davison, A. C., Padoan, S., and Ribatet, M. (2012), “Statistical Modelling of Spatial Extremes,” (with Discussion), Statistical Science, 27, 161–186. DOI: 10.1214/11-STS376.
  • de Fondeville, R., and Davison, A. C. (2018), “High-Dimensional Peaks-Over-Threshold Inference,” Biometrika, 105, 575–592. DOI: 10.1093/biomet/asy026.
  • de Haan, L. (1984), “A Spectral Representation for Max-Stable Processes,” Annals of Probability, 12, 1194–1204.
  • Dombry, C., Engelke, S., and Oesting, M. (2017), “Bayesian Inference for Multivariate Extreme Value Distributions,” Electronic Journal of Statistics, 11, 4813–4844. DOI: 10.1214/17-EJS1367.
  • Donlon, C. J., Martin, M., Stark, J., Roberts-Jones, J., Fiedler, E., and Wimmer, W. (2012), “The Operational Sea Surface Temperature and Sea Ice Analysis (OSTIA) System,” Remote Sensing of Environment, 116, 140–158. DOI: 10.1016/j.rse.2010.10.017.
  • Einmahl, J. H. J., Kiriliouk, A., Krajina, A., and Segers, J. (2016), “An M-estimator of Spatial Tail Dependence,” Journal of the Royal Statistical Society, Series B, 78, 275–298. DOI: 10.1111/rssb.12114.
  • Engelke, S., and Hitz, A. S. (2020), “Graphical Models for Extremes,” (with Discussion), Journal of the Royal Statistical Society, Series B, 82, 871–932. DOI: 10.1111/rssb.12355.
  • Engelke, S., and Ivanovs, J. (2021), “Sparse Structures for Multivariate Extremes,” Annual Review of Statistics and its Application, 8, 241–270. DOI: 10.1146/annurev-statistics-040620-041554.
  • Fraser, D. A. S., and Reid, N. (2020), “Combining Likelihood and Significance Functions,” Statistica Sinica, 30, 1–15. DOI: 10.5705/ss.202016.0508.
  • Genton, M. G., Ma, Y., and Sang, H. (2011), “On the Likelihood Function of Gaussian Max-Stable Processes,” Biometrika, 98, 481–488. DOI: 10.1093/biomet/asr020.
  • Guinness, J. (2018), “Permutation and Grouping Methods for Sharpening Gaussian Process Approximations,” Technometrics, 60, 415–429. DOI: 10.1080/00401706.2018.1437476.
  • Gumbel, E. J. (1960), “Distributions de valeurs extrêmes en plusieurs dimensions,” Publication de l’Institut de Statistique de l’Universié de Paris, 9, 171–173.
  • Gumbel, E. J. (1961), “Bivariate Logistic Distributions,” Journal of the American Statistical Association, 56, 335–349. DOI: 10.1080/01621459.1961.10482117.
  • Hazra, A., and Huser, R. (2021), “Estimating High-Resolution Red Sea Surface Temperature Hotspots, Using a Low-Rank Semiparametric Spatial Model,” Annals of Applied Statistics, 15, 572–596.
  • Huser, R. (2013), “Statistical Modeling and Inference for Spatio-Temporal Extremes,” Ph.D. thesis, École Polytechnique Fédérale de Lausanne.
  • ——- (2021), “Editorial: EVA 2019 Data Competition on Spatio-Temporal Prediction of Red Sea Surface Temperature Extremes,” Extremes, 24, 91–104.
  • Huser, R., and Davison, A. C. (2013), “Composite Likelihood Estimation for the Brown–Resnick Process,” Biometrika, 100, 511–518. DOI: 10.1093/biomet/ass089.
  • ——- (2014), “Space-Time Modelling of Extreme Events,” Journal of the Royal Statistical Society, Series B, 76, 439–461.
  • Huser, R., Davison, A. C., and Genton, M. G. (2016), “Likelihood Estimators for Multivariate Extremes,” Extremes, 19, 79–103. DOI: 10.1007/s10687-015-0230-4.
  • Huser, R., Dombry, C., Ribatet, M., and Genton, M. G. (2019), “Full Likelihood Inference for Max-Stable Data,” Stat, 8, e218. DOI: 10.1002/sta4.218.
  • Huser, R., and Genton, M. G. (2016), “Non-Stationary Dependence Structures for Spatial Extremes, Journal of Agricultural, Biological and Environmental Statistics, 21, 470–491. DOI: 10.1007/s13253-016-0247-4.
  • Hüsler, J., and Reiss, R. D. (1989), “Maxima of Normal Random Vectors: Between Independence and Complete Dependence,” Statistics & Probability Letters, 7, 283–286. DOI: 10.1016/0167-7152(89)90106-5.
  • Kabluchko, Z., Schlather, M., and de Haan, L. (2009), “Stationary Max-Stable Fields Associated to Negative Definite Functions,” Annals of Probability, 37, 2042–2065.
  • Katzfuss, M., and Guinness, J. (2021), “A General Framework for Vecchia Approximations of Gaussian Processes,” Statistical Science, 36, 124–141. DOI: 10.1214/19-STS755.
  • Katzfuss, M., Guinness, J., Gong, W., and Zilber, D. (2020), “Vecchia Approximations of Gaussian-Process Predictions,” Journal of Agricultural, Biological and Environmental Statistics, 25, 383–414. DOI: 10.1007/s13253-020-00401-7.
  • Lenzi, A., Bessac, J., Rudi, J., and Stein, M. L. (2023), “Neural Networks for Parameter Estimation in Intractable Models,” Computational Statistics and Data Analysis, 185, 107762. DOI: 10.1016/j.csda.2023.107762.
  • Lindgren, F., Rue, H., and Lindström, J. (2011), “An Explicit Link between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach,” Journal of the Royal Statistical Society, Series B, 73, 423–498. DOI: 10.1111/j.1467-9868.2011.00777.x.
  • Nascimento, M., and Shaby, B. A. (2022), “A Vecchia Approximation for High-Dimensional Gaussian Cumulative Distribution Functions Arising from Spatial Data,” Journal of Statistical Computation and Simulation, 92, 1977–1994. DOI: 10.1080/00949655.2021.2016759.
  • Opitz, T. (2013), “Extremal t Processes: Elliptical Domain of Attraction and a Spectral Representation,” Journal of Multivariate Analysis, 122, 409–413. DOI: 10.1016/j.jmva.2013.08.008.
  • Pace, L., Salvan, A., and Sartori, N. (2019), “Efficient Composite Likelihood for a Scalar Parameter of Interest,” Stat, 8, e222. DOI: 10.1002/sta4.222.
  • Padoan, S. A., Ribatet, M., and Sisson, S. A. (2010), “Likelihood-based Inference for Max-Stable Processes,” Journal of the American Statistical Association, 105, 263–277. DOI: 10.1198/jasa.2009.tm08577.
  • Papastathopoulos, I., and Strokorb, K. (2016), “Conditional Independence among Max-Stable Laws,” Statistics & Probability Letters, 108, 9–15. DOI: 10.1016/j.spl.2015.08.008.
  • Reich, B. J., and Shaby, B. A. (2012), “A Hierarchical Max-Stable Spatial Model for Extreme Precipitation,” Annals of Applied Statistics, 6, 1430–1451. DOI: 10.1214/12-AOAS591.
  • Rue, H., and Held, L. (2005), Gaussian Markov Random Fields: Theory and Applications, Monographs on Statistics and Applied Probability (Vol. 104), London: Chapman & Hall.
  • Sainsbury-Dale, M., Zammit-Mangion, A., and Huser, R. (2023), “Likelihood-Free Parameter Estimation with Neural Bayes Estimators,” The American Statistician, to appear. DOI: 10.1080/00031305.2023.2249522.
  • Sang, H., and Genton, M. G. (2014), “Tapered Composite Likelihood for Spatial Max-Stable Models,” Spatial Statistics, 8, 86–103. DOI: 10.1016/j.spasta.2013.07.003.
  • Schäfer, F., Katzfuss, M., and Owhadi, H. (2021), “Sparse Cholesky Factorization by Kullback–Leibler Minimization,” SIAM Journal on Scientific Computing, 43, A2019–A2046. DOI: 10.1137/20M1336254.
  • Segers, J. (2012), “Max-Stable Models for Multivariate Extremes,” REVSTAT. 10, 61–82.
  • Shi, D. (1995), “Fisher Information for a Multivariate Extreme Value Distribution,” Biometrika, 82, 644–649. DOI: 10.1093/biomet/82.3.644.
  • Stein, M. L., Chi, Z., and Welty, L. J. (2004), “Approximating Likelihoods for Large Spatial Data Sets,” Journal of the Royal Statistical Society, Series B, 66, 275–296. DOI: 10.1046/j.1369-7412.2003.05512.x.
  • Stephenson, A., and Tawn, J. A. (2005), “Exploiting Occurrence Times in Likelihood Inference for Componentwise Maxima,” Biometrika, 92, 213–227. DOI: 10.1093/biomet/92.1.213.
  • Stephenson, A. G., Shaby, B. A., Reich, B. J., and Sullivan, A. L. (2015), “Estimating Spatially Varying Severity Thresholds of a Forest Fire Danger Rating System Using Max-Stable Extreme-Event Modeling,” Journal of Applied Meteorology and Climatology, 54, 395–407. DOI: 10.1175/JAMC-D-14-0041.1.
  • Thibaud, E., Aalto, J., Cooley, D. S., Davison, A. C., and Heikkinen, J. (2016), “Bayesian Inference for the Brown–Resnick Process, with an Application to Extreme Low Temperatures,” Annals of Applied Statistics, 10, 2303–2324.
  • Tittensor, D. P., Novaglio, C., Harrison, C. S., Heneghan, R. F., Barrier, N., Bianchi, D., et al. (2021), “Next-Generation Ensemble Projections Reveal Higher Climate Risks for Marine Ecosystems,” Nature Climate Change, 11, 973–981. DOI: 10.1038/s41558-021-01173-9.
  • Varin, C., Reid, N., and Firth, D. (2011), “An Overview of Composite Likelihood Methods,” Statistica Sinica, 21, 5–42.
  • Vecchia, A. V. (1988), “Estimation and Model Identification for Continuous Spatial Processes,” Journal of the Royal Statistical Society, Series B, 50, 297–312. DOI: 10.1111/j.2517-6161.1988.tb01729.x.
  • Vettori, S., Huser, R., and Genton, M. G. (2019), “Bayesian Modeling of Air Pollution Extremes Using Nested Multivariate Max-Stable Processes,” Biometrics, 75, 831–841. DOI: 10.1111/biom.13051.
  • Vettori, S., Huser, R., Segers, J., and Genton, M. G. (2020), “Bayesian Model Averaging Over Tree-based Dependence Structures for Multivariate Extremes,” Journal of Computational and Graphical Statistics, 29, 174–190. DOI: 10.1080/10618600.2019.1647847.
  • Wadsworth, J. L. (2015), “On the Occurrence Times of Componentwise Maxima and Bias in Likelihood Inference for Multivariate Max-Stable Distributions,” Biometrika, 102, 705–711. DOI: 10.1093/biomet/asv029.
  • Wadsworth, J. L., and Tawn, J. A. (2014), “Efficient Inference for Spatial Extreme Value Processes Associated to Log-Gaussian Random Functions,” Biometrika, 101, 1–15. DOI: 10.1093/biomet/ast042.
  • Whitaker, T., Beranger, B., and Sisson, S. A. (2020), “Composite Likelihood Methods for Histogram-Valued Random Variables,” Statistics and Computing, 30, 1459–1477. DOI: 10.1007/s11222-020-09955-5.
  • Zhong, P., Huser, R., and Opitz, T. (2022), “Modeling Non-stationary Temperature Maxima based on Extremal Dependence Changing with Event Magnitude,” Annals of Applied Statistics, 16, 272–299.