Model‐based inference of conditional extreme value distributions with hydrological applications

Abstract

Multivariate extreme value models are used to estimate joint risk in a number of applications, with a particular focus on environmental fields ranging from climatology and hydrology to oceanography and seismic hazards. The semi‐parametric conditional extreme value model of Heffernan and Tawn involving a multivariate regression provides the most suitable of current statistical models in terms of its flexibility to handle a range of extremal dependence classes. However, the standard inference for the joint distribution of the residuals of this model suffers from the curse of dimensionality because, in a d‐dimensional application, it involves a d−1‐dimensional nonparametric density estimator, which requires, for accuracy, a number points and commensurate effort that is exponential in d. Furthermore, it does not allow for any partially missing observations to be included, and a previous proposal to address this is extremely computationally intensive, making its use prohibitive if the proportion of missing data is nontrivial. We propose to replace the d−1‐dimensional nonparametric density estimator with a model‐based copula with univariate marginal densities estimated using kernel methods. This approach provides statistically and computationally efficient estimates whatever the dimension, d, or the degree of missing data. Evidence is presented to show that the benefits of this approach substantially outweigh potential misspecification errors. The methods are illustrated through the analysis of UK river flow data at a network of 46 sites and assessing the rarity of the 2015 floods in North West England.

Multivariate statistical modelling of the drivers of compound flood events in south Florida

“…The long-term mean sea level signal is superimposed onto inter-annual to multi-decadal sea level variability caused by tidal modulations associated with the nodal (18.61 year) and perigean (8.5 year) cycles, as well as other oceanic-atmospheric processes (e.g. Valle-Levinson et al, 2017). Here, a moving window approach is applied to the O-sWL series to remove long-term sea level rise and seasonality effects (Arns et al, 2013).…”

“…The parameters a and b are estimated using maximum likelihood under the temporary assumption that Z is normally distributed with unknown mean and variance. Recently, Towe et al (2019) removed the temporary Gaussian assumption on the joint residual distribution by instead modelling the distribution semiparametrically using a Gaussian copula and kernel-densityestimated marginals. This alteration permits new combinations of Z to arise, thus enabling non-deterministic extrapolation of past events; in the context of the present study this is to be considered in future work.…”

Assessing the risk of disruption of wind turbine operations in Saudi Arabia using Bayesian spatial extremes

“…The so-called near-independence models (e.g., Tawn, 1996, 1997;Heffernan and Tawn, 2004;Ramos and Ledford, 2009) for spatial extremal data have also been developed to capture the decreasing dependence for increasing rare events that classical models are not able to capture. For example, the conditional extremes model of Heffernan and Tawn (2004) has been used in several stud-ies on spatial extremes (e.g., Winter et al, 2016;Towe et al, 2019). An alternative method for modeling spatial extremes by borrowing strength across locations is regional frequency analysis (RFA) by Hosking and Wallis (1997) as applied in Weiss et al (2014).…”

Modeling short‐ranged dependence in block extrema with application to polar temperature data

“…Extreme value theory (EVT) provides a probabilistic framework for performing statistical inference on the far upper tail of distributions, and is therefore useful in a wide variety of environmental applications. Examples include modeling extreme temperatures (Huang, Stein, McInerney, & Moyer, 2016; O'Sullivan, Sweeney, & Parnell, 2020; Stein, 2020a, 2020b), precipitation extremes (Fix, Cooley, & Thibaud, 2020; Hazra, Reich, & Staicu, 2020; Huang, Nychka, & Zhang, 2019; Russell, Risser, Smith, & Kunkel, 2020), and extremes in hydrology (Beck, Genest, Jalbert, & Mailhot, 2020; Towe, Tawn, Lamb, & Sherlock, 2019).…”