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