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Activity Number: 39 - Recent Advancements in the Analysis of Extremes
Type: Contributed
Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics and the Environment
Abstract #305170
Title: Flexible Sub-Asymptotic Modeling of Threshold Exceedances Using Hierarchical Ratio Models
Author(s): Rishikesh Yadav* and Raphaël Huser and Thomas Opitz
Companies: King Abdullah University of Science and Technology (KAUST) and King Abdullah University of Science and Technology and INRA
Keywords: Extended generalized Pareto distribution; extreme events; threshold exceedance; sub-asymptotic modeling

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 without losing much flexibility. Spatial dependence can be incorporated at the level of the latent process, assuming that the observed data are conditionally independent. We design penalized complexity priors for crucial model parameters to shrink our model toward a simple GP distribution of reference. We fit our models in fairly high dimensions using an MCMC algorithm with proposal distributions based on the Metropolis-adjusted Langevin algorithm (MALA). We develop an adaptive scheme to calibrate the MALA tuning parameters. Our models avoid the expensive numerical evaluations of multifold integrals in censored likelihood expressions. We demonstrate our new methodology via simulation, and by application to air pollution data in Western United States.

Authors who are presenting talks have a * after their name.

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