  The EVA 2023 data competition consisted of four challenges, ranging from
interval estimation for very high quantiles of univariate extremes conditional
on covariates, point estimation of unconditional return levels under a custom
loss function, to estimation of the probabilities of tail events for low and
high-dimensional multivariate data. We tackle these tasks by revisiting the
current and existing literature on conditional univariate and multivariate
extremes. We propose new cross-validation methods for covariate-dependent
models, validation metrics for exchangeable multivariate models, formulae for
the joint probability of exceedance for multivariate generalized Pareto vectors
and a composition sampling algorithm for generating multivariate tail events
for the latter. We highlight overarching themes ranging from model validation
at extremely high quantile levels to building custom estimation strategies that
leverage model assumptions.
