Ahmed,, M., Maume‐Deschamps,, V., Ribereau,, P., & Vial,, C. (2019). Spatial risk measures for max‐stable and max‐mixture processes. Stochastics, 92(7), 1005–1020.

Azzalini,, A., & Capitanio,, A. (2003). Distributions generated by perturbation of symmetry with emphasis on a multivariate skew *t*‐distribution. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65, 367–389.

Bacro,, J.‐N., Gaetan,, C., Opitz,, T., & Toulemonde,, G. (2020). Hierarchical space–time modeling of asymptotically independent exceedances with an application to precipitation data. Journal of the American Statistical Association, 115, 555–569.

Bacro,, J.‐N., Gaetan,, C., & Toulemonde,, G. (2016). A flexible dependence model for spatial extremes. Journal of Statistical Planning and Inference, 172, 36–52.

Bakka,, H., Rue,, H., Fuglstad,, G.‐A., Riebler,, A., Bolin,, D., Illian,, J., … Lindgren,, F. (2018). Spatial modeling with R‐INLA: A review. WIREs: Computational Statistics, 10, e1443.

Barndorff‐Nielsen,, O. (1977). Exponentially decreasing distributions for the logarithm of particle size. Proceedings of the Royal Society A: Mathematical Physical and Engineering Sciences, 353, 401–419.

Barndorff‐Nielsen,, O. (1978). Hyperbolic distributions and distributions on hyperbolae. Scandinavian Journal of Statistics, 5, 151–157.

Beirlant,, J., Goegebeur,, Y., Segers,, J., & Teugels,, J. (2004). Statistics of extremes: Theory and applications. Chichester: Wiley.

Beranger,, B., Stephenson,, A. G., & Sisson,, S. A. (2020). High‐dimensional inference using the extremal skew‐*t* process. Extremes. https://doi.org/10.1007/s10687-020-00376-1.

Blanchet,, J., & Davison,, A. C. (2011). Spatial modelling of extreme snow depth. Annals of Applied Statistics, 5, 1699–1725.

Bopp,, G. P., & Shaby,, B. A. (2017). An exponential‐gamma mixture model for extreme Santa Ana winds. Environmetrics, 28, e2476.

Bopp,, G. P., Shaby,, B. A., Forest,, C. E., & Mejía,, A. (2020). Projecting flood‐inducing precipitation with a Bayesian analogue model. Journal of Agricultural, Biological and Environmental Statistics, 25, 229–249.

Bopp,, G. P., Shaby,, B. A., & Huser,, R. (2020). A hierarchical max‐infinitely divisible spatial model for extreme precipitation. Journal of American Statistical Association. https://10.1080/01621459.2020.1750414.

Brown,, B. M., & Resnick,, S. I. (1977). Extreme values of independent stochastic processes. Journal of Applied Probability, 14, 732–739.

Buishand,, T. A., de Haan,, L., & Zhou,, C. (2008). On spatial extremes: With application to a rainfall problem. Annals of Applied Statistics, 2, 624–642.

Cao,, J., Genton,, M. G., Keyes,, D. E., & Turkiyyah,, G. M. (2019). Hierarchical‐block conditioning approximations for high‐dimensional multivariate normal probabilities. Statistics and Computing, 29, 585–598.

Casson,, E., & Coles,, S. (1999). Spatial regression models for extremes. Extremes, 1, 449–468.

Castro‐Camilo,, D., de Carvalho,, M., & Wadsworth,, J. L. (2018). Time‐varying extreme value dependence with application to leading European stock markets. Annals of Applied Statistics, 12, 283–309.

Castro‐Camilo,, D., & Huser,, R. (2020). Local likelihood estimation of complex tail dependence structures, applied to U.S. precipitation extremes. Journal of the American Statistical Association, 115, 1037–1054.

Castro‐Camilo,, D., Huser,, R., & Rue,, H. (2019). A spliced gamma‐generalized Pareto model for short‐term extreme wind speed probabilistic forecasting. Journal of Agricultural, Biological and Environmental Statistics, 24, 517–534.

Castruccio,, S., Huser,, R., & Genton,, M. G. (2016). High‐order composite likelihood inference for max‐stable distributions and processes. Journal of Computational and Graphical Statistics, 25, 1212–1229.

Chavez‐Demoulin,, V., & Davison,, A. C. (2005). Generalized additive modelling of sample extremes. Journal of the Royal Statistical Society: Series C (Applied Statistics), 54, 207–222.

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

Cooley,, D. S., Cisewski,, J., Erhardt,, R. J., Jeon,, S., Mannshardt‐Shamseldin,, E. C., Omolo,, B. O., & Sun,, Y. (2012). A survey of spatial extremes: Measuring spatial dependence and modeling spatial effects. REVSTAT, 10, 135–165.

Cooley,, D. S., Hunter,, B. D., & Smith,, R. L. (2019). Univariate and multivariate extremes for the environmental sciences. In A. E. Gelfand,, M. Fuentes,, J. A. Hoeting,, & R. L. Smith, (Eds.), Handbook of environmental and ecological statistics (pp. 153–180). Boca Raton, FL: CRC Press.

Cooley,, D. S., Naveau,, P., & Nychka,, D. (2007). Bayesian spatial modeling of extreme precipitation return levels. Journal of American Statistical Association, 102, 824–840.

Cooley,, D. S., & Sain,, S. R. (2010). Spatial hierarchical modeling of precipitation extremes from a regional climate model. Journal of Agricultural, Biological, and Environmental Statistics, 15, 381–402.

Davison,, A. C., & Gholamrezaee,, M. M. (2012). Geostatistics of extremes. Proceedings of the Royal Society A: Mathematical, Physical %26 Engineering Sciences, 468, 581–608.

Davison,, A. C., & Huser,, R. (2015). Statistics of extremes. Annual Review of Statistics and its Application, 2, 203–235.

Davison,, A. C., Huser,, R., & Thibaud,, E. (2013). Geostatistics of dependent and asymptotically independent extremes. Mathematical Geosciences, 45, 511–529.

Davison,, A. C., Huser,, R., & Thibaud,, E. (2019). Spatial extremes. In A. E. Gelfand,, M. Fuentes,, J. A. Hoeting,, & R. L. Smith, (Eds.), Handbook of environmental and ecological statistics (pp. 711–744). Boca Raton, FL: CRC Press.

Davison,, A. C., Padoan,, S., & Ribatet,, M. (2012). Statistical modelling of spatial extremes (with discussion). Statistical Science, 27, 161–186.

Davison,, A. C., & Smith,, R. L. (1990). Models for exceedances over high thresholds (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 52, 393–442.

de Fondeville,, R., & Belzile,, L. (2018) *mvPot: Multivariate peaks‐over‐threshold modelling for spatial extreme events*. R package version 0.1.4.

de Fondeville,, R., & Davison,, A. C. (2018). High‐dimensional peaks‐over‐threshold inference. Biometrika, 105, 575–592.

de Haan,, L. (1984). A spectral representation for max‐stable processes. Annals of Probability, 12, 1194–1204.

de Haan,, L., & Ferreira,, A. (2006). Extreme value theory: An introduction. New York: Springer.

Dieker,, A. B., & Mikosch,, T. (2015). Exact simulation of Brown–Resnick random fields at a finite number of locations. Extremes, 18, 301–314.

Dombry,, C., Engelke,, S., & Oesting,, M. (2016). Exact simulation of max‐stable processes. Biometrika, 103, 303–317.

Dombry,, C., Engelke,, S., & Oesting,, M. (2017). Bayesian inference for multivariate extreme value distributions. Electronic Journal of Statistics, 11, 4813–4844.

Dombry,, C., Éyi‐Minko,, F., & Ribatet,, M. (2013). Conditional simulation of max‐stable processes. Biometrika, 100, 111–124.

Dombry,, C., & Ribatet,, M. (2015). Functional regular variations, Pareto processes and peaks over threshold. Statistics and its Interface, 8, 9–17.

Dyrrdal,, A. V., Lenkoski,, A., Thorarinsdottir,, T. L., & Stordal,, F. (2015). Bayesian hierarchical modeling of extreme hourly precipitation in Norway. Environmetrics, 26, 89–106.

Eastoe,, E. F., & Tawn,, J. A. (2009). Modelling non‐stationary extremes with application to surface level ozone. Journal of the Royal Statistical Society: Series C (Applied Statistics), 58, 25–45.

Embrechts,, P., Klüppelberg,, C., & Mikosch,, T. (1997). Modelling extremal events for insurance and finance. Berlin: Springer.

Engelke,, S., & Hitz,, A. S. (2020). Graphical models for multivariate extremes (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 82, 871–932.

Engelke,, S., & Ivanovs,, J. (in press). Sparse structures for multivariate extremes. Annual Review of Statistics and its Application 8.

Engelke,, S., Opitz,, T., & Wadsworth,, J. L. (2019). Extremal dependence of random scale constructions. Extremes, 22, 623–666.

Ferreira,, A., & de Haan,, L. (2014). The generalized Pareto process; with a view towards application and simulation. Bernoulli, 20, 1717–1737.

Geirsson,, Ó. P., Hrafnkelsson,, B., & Simpson,, D. (2015). Computationally efficient spatial modeling of annual maximum 24‐h precipitation on a fine grid. Environmetrics, 26, 339–353.

Genton,, M. G., Keyes,, D. E., & Turkiyyah,, G. M. (2018). Hierarchical decompositions for the computation of high‐dimensional multivariate normal probabilities. Journal of Computational and Graphical Statistics, 27, 268–277.

Gilleland,, E., Brown,, B. G., & Ammann,, C. M. (2013). Spatial extreme value analysis to project extremes of large‐scale indicators for severe weather. Environmetrics, 24, 418–432.

Giné,, E., Hahn,, M. G., & Vatan,, P. (1990). Max‐infinitely divisible and max‐stable sample continuous processes. Probability Theory and Related Fields, 87, 139–165.

Hazra,, A., Reich,, B. J., & Staicu,, A.‐M. (2019). A multivariate spatial skew‐*t* process for joint modeling of extreme precipitation indexes. Environmetrics, 31, e2602.

Heffernan,, J. E., & Resnick,, S. I. (2007). Limit laws for random vectors with an extreme component. Annals of Applied Probability, 17, 537–571.

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

Hrafnkelsson,, B., Siegert,, S., Huser,, R., Bakka,, H., & Jóhannesson,, A. V. (in press). Max‐and‐smooth: A two‐step approach for approximate Bayesian inference in latent Gaussian models. Bayesian Analysis. https://doi.org/10.1214/20-BA1219.

Hua,, L., & Joe,, H. (2011). Tail order and intermediate tail dependence of multivariate copulas. Journal of Multivariate Analysis, 102, 1454–1471.

Huser,, R., & Davison,, A. C. (2014). Space‐time modelling of extreme events. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76, 439–461.

Huser,, R., Davison,, A. C., & Genton,, M. G. (2016). Likelihood estimators for multivariate extremes. Extremes, 19, 79–103.

Huser,, R., Dombry,, C., Ribatet,, M., & Genton,, M. G. (2019). Full likelihood inference for max‐stable data. Stat, 8, e218.

Huser,, R., & Genton,, M. G. (2016). Non‐stationary dependence structures for spatial extremes. Journal of Agricultural, Biological and Environmental Statistics, 21, 470–491.

Huser,, R., Opitz,, T., & Thibaud,, E. (2017). Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures. Spatial Statistics, 21, 166–186.

Huser,, R., Opitz,, T., & Thibaud,, E. (in press). Max‐infinitely divisible models and inference for spatial extremes. Scandinavian Journal of Statistics. https://doi.org/10.1111/sjos.12491.

Huser,, R., & Wadsworth,, J. L. (2019). Modeling spatial processes with unknown extremal dependence class. Journal of the American Statistical Association, 114, 434–444.

Jonathan,, P., & Ewans,, K. (2013). Statistical modelling of extreme ocean environments for marine design: A review. Ocean Engineering, 62, 91–109.

Jonathan,, P., Randell,, D., Wu,, Y., & Ewans,, K. (2014). Return level estimation from non‐stationary spatial data exhibiting multidimensional covariate effects. Ocean Engineering, 88, 520–532.

Kabluchko,, Z., & Schlather,, M. (2010). Ergodic properties of max‐infinitely divisible processes. Stochastic Processes and their Applications, 120, 281–295.

Kabluchko,, Z., Schlather,, M., & de Haan,, L. (2009). Stationary max‐stable fields associated to negative definite functions. Annals of Probability, 37, 2042–2065.

Katz,, R. W., Parlange,, M., & Naveau,, P. (2002). Statistics of extremes in hydrology. Advances in Water Resources, 25, 1287–1304.

Krupskii,, P., & Genton,, M. G. (2017). Factor copula models for data with spatio‐temporal dependence. Spatial Statistics, 22, 180–195.

Krupskii,, P., Huser,, R., & Genton,, M. G. (2018). Factor copula models for replicated spatial data. Journal of American Statistical Association, 113, 467–479.

Krupskii,, P., & Joe,, H. (2013). Factor copula models for multivariate data. Journal of Multivariate Analysis, 120, 85–101.

Ledford,, A. W., & Tawn,, J. A. (1996). Statistics for near independence in multivariate extreme values. Biometrika, 83, 169–187.

Liu,, Z., Blanchet,, J. H., Dieker,, A. B., & Mikosch,, T. (2019). On logarithmically optimal exact simulation of max‐stable and related random fields on a compact set. Bernoulli, 25, 2949–2981.

Morris,, S. A., Reich,, B. J., Thibaud,, E., & Cooley,, D. (2017). A space‐time skew‐*t* model for threshold exceedances. Biometrics, 73, 749–758.

Northrop,, P. J., & Jonathan,, P. (2011). Threshold modelling of spatially‐dependent non‐stationary extremes with application to hurricane‐induced wave heights (with discussion). Environmetrics, 22, 799–809.

Oesting,, M., Kabluchko,, Z., & Schlather,, M. (2012). Simulation of Brown–Resnick processes. Extremes, 15, 89–107.

Oesting,, M., Schlather,, M., & Friederichs,, P. (2017). Statistical post‐processing of forecasts for extremes using bivariate Brown–Resnick processes with an application to wind gusts. Extremes, 20, 309–332.

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

Opitz,, T. (2016). Modeling asymptotically independent spatial extremes based on Laplace random fields. Spatial Statistics, 16, 1–18.

Opitz,, T. (2017). Latent Gaussian modeling and INLA: A review with focus on space–time applications. Journal de la Société Française de Statistique, 158, 62–85.

Opitz,, T., Huser,, R., Bakka,, H., & Rue,, H. (2018). INLA goes extreme: Bayesian tail regression for the estimation of high spatio‐temporal quantiles. Extremes, 21, 441–462.

Padoan,, S. A. (2013). Extreme dependence models based on event magnitude. Journal of Multivariate Analysis, 122, 1–19.

Padoan,, S. A., Ribatet,, M., & Sisson,, S. A. (2010). Likelihood‐based inference for max‐stable processes. Journal of the American Statistical Association, 105, 263–277.

Reich,, B. J., & Shaby,, B. A. (2012). A hierarchical max‐stable spatial model for extreme precipitation. Annals of Applied Statistics, 6, 1430–1451.

Reich,, B. J., & Shaby,, B. A. (2019). A spatial Markov model for climate extremes. Journal of Computational and Graphical Statistics, 28, 117–126.

Reiss,, R.‐D., & Thomas,, M. (2007). Statistical analysis of extreme values (3rd ed.). Basel: Birkhäuser.

Resnick,, S. I. (1987). Extreme values, regular variation and point processes. New York: Springer.

Ribatet,, M. (2013). Spatial extremes: Max‐stable processes at work. Journal de la Société Française de Statistique, 154, 156–177.

Ribatet,, M., Cooley,, D. S., & Davison,, A. C. (2012). Bayesian inference from composite likelihoods, with an application to spatial extremes. Statistica Sinica, 22, 813–845.

Risser,, M. D., & Wehner,, M. F. (2017). Attributable human‐induced changes in the likelihood and magnitude of the observed extreme precipitation during Hurricane Harvey. Geophysical Research Letters, 44, 12457–12464.

Rootzén,, H., Segers,, J., & Wadsworth,, J. L. (2018a). Multivariate peaks over thresholds models. Extremes, 21, 115–145.

Rootzén,, H., Segers,, J., & Wadsworth,, J. L. (2018b). Multivariate generalized Pareto distributions: Parametrizations, representations, and properties. Journal of Multivariate Analysis, 165, 117–131.

Rootzén,, H., & Tajvidi,, N. (2006). Multivariate generalized Pareto distributions. Bernoulli, 12, 917–930.

Rue,, H., Martino,, S., & Chopin,, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society (Series B), 71, 319–392.

Rue,, H., Riebler,, A., Sørbye,, S. H., Illian,, J. B., Simpson,, D. P., & Lindgren,, F. K. (2017). Bayesian computing with INLA: A review. Annual Review of Statistics and its Application, 4, 395–421.

Sampson,, P. D., & Guttorp,, P. (1992). Nonparametric estimation of nonstationary spatial covariance structure. Journal of the American Statistical Association, 87, 108–119.

Sang,, H., & Gelfand,, A. (2009). Hierarchical modeling for extreme values observed over space and time. Environmental and Ecological Statistics, 16, 407–426.

Sang,, H., & Gelfand,, A. (2010). Continuous spatial process models for spatial extreme values. Journal of Agricultural, Biological and Environmental Statistics, 15, 49–65.

Schär,, C. (2016). Climate extremes: The worst heat waves to come. Nature Climate Change, 6, 128–129.

Schlather,, M. (2002). Models for stationary max‐stable random fields. Extremes, 5, 33–44.

Schlather,, M., & Tawn,, J. A. (2003). A dependence measure for multivariate and spatial extreme values: Properties and inference. Biometrika, 90, 139–156.

Segers,, J. (2012). Max‐stable models for multivariate extremes. REVSTAT, 10, 61–82.

Shooter,, R., Ross,, E., Tawn,, J. A., & Jonathan,, P. (2019). On spatial conditional extremes for ocean storm severity. Environmetrics, 30(6), e2562.

Sibuya,, M. (1960). Bivariate extreme statistics, I. Annals of the Institute of Statistical Mathematics, 11, 195–210.

Smith,, A. B., & Katz,, R. W. (2013). US billion‐dollar weather and climate disasters: Data sources, trends, accuracy and biases. Natural Hazards, 67, 387–410.

Stephenson,, A., & Tawn,, J. A. (2005). Exploiting occurrence times in likelihood inference for componentwise maxima. Biometrika, 92, 213–227.

Stephenson,, A. G., Shaby,, B. A., Reich,, B. J., & 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.

Thibaud,, E., Aalto,, J., Cooley,, D. S., Davison,, A. C., & Heikkinen,, J. (2016). Bayesian inference for the Brown–Resnick process, with an application to extreme low temperatures. Annals of Applied Statistics, 10, 2303–2324.

Thibaud,, E., Mutzner,, R., & Davison,, A. C. (2013). Threshold modeling of extreme spatial rainfall. Water Resources Research, 49, 4633–4644.

Thibaud,, E., & Opitz,, T. (2015). Efficient inference and simulation for elliptical Pareto processes. Biometrika, 102, 855–870.

Turkman,, K. F., Turkman,, M. A. A., & Pereira,, J. M. (2010). Asymptotic models and inference for extremes of spatio‐temporal data. Extremes, 13, 375–397.

Varin,, C., Reid,, N., & Firth,, D. (2011). An overview of composite likelihood methods. Statistica Sinica, 21, 5–42.

Varin,, C., & Vidoni,, P. (2005). A note on composite likelihood inference and model selection. Biometrika, 92, 519–528.

Vettori,, S., Huser,, R., & Genton,, M. G. (2019). Bayesian modeling of air pollution extremes using nested multivariate max‐stable processes. Biometrics, 75, 831–841.

Vettori,, S., Huser,, R., Segers,, J., & Genton,, M. G. (2020). Bayesian model averaging over tree‐based dependence structures for multivariate extremes. Journal of Computational and Graphical Statistics, 29, 174–190.

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.

Wadsworth,, J. L., & Tawn,, J. A. (2012). Dependence modelling for spatial extremes. Biometrika, 99, 253–272.

Wadsworth,, J. L., & Tawn,, J. A. (2014). Efficient inference for spatial extreme value processes associated to log‐Gaussian random functions. Biometrika, 101, 1–15.

Wadsworth,, J. L., & Tawn,, J. A. (2019) *Higher‐dimensional spatial extremes via single‐site conditioning*. arXiv preprint 1912.06560.

Wadsworth,, J. L., Tawn,, J. A., Davison,, A. C., & Elton,, D. M. (2017). Modelling across extremal dependence classes. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79, 149–175.