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Abstract:
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In this paper, we develop new flexible univariate tail models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the generalized Pareto (GP) limit for univariate threshold exceedances. These models can accommodate departure from asymptotic threshold stability in finite samples while keeping the asymptotic GP distribution as a special (or boundary) case and can be used to model the tails and the bulk regions jointly. Spatial dependence is modeled through a latent process, while the data are assumed to be conditionally independent. We fit our models in fairly high dimensions based on Markov chain Monte Carlo by exploiting the Metropolis-adjusted Langevin algorithm (MALA), which guarantees fast convergence of Markov chains. We also develop an adaptive scheme to calibrate the MALA tuning parameters. Furthermore, our models avoid the expensive numerical evaluations of multifold integrals in censored likelihood expressions. We demonstrate our new methodology by simulation and application to a dataset of extreme rainfall episodes that occurred in Germany. If time allows, we will extend this framework to the modeling of spatio-temporal extremes.
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