Spatial hierarchical modeling of threshold exceedances using rate mixtures

Rishikesh Yadav, Raphaël Huser, Thomas Opitz

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We develop new exible univariate models for light-tailed and heavy-tailed data, which extend a hierarchical representation of the generalized Pareto (GP) limit for 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 capture the tails and the bulk jointly without losing much exibility. Spatial dependence is modeled through a latent process, while the data are assumed to be conditionally independent. Focusing on a gamma-gamma model construction, we design penalized complexity priors for crucial model parameters, shrinking our proposed spatial Bayesian hierarchical model toward a simpler reference whose marginal distributions are GP with moderately heavy tails. Our model can be fitted in fairly high dimensions using Markov chain Monte Carlo by exploiting the Metropolis-adjusted Langevin algorithm (MALA), which guarantees fast convergence of Markov chains with efficient block proposals for the latent variables. We also develop an adaptive scheme to calibrate the MALA tuning parameters. Moreover, our model avoids 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 events that occurred in Germany. Our fitted gamma-gamma model provides a satisfactory performance and can be successfully used to predict rainfall extremes at unobserved locations.
Original languageEnglish (US)
StatePublished - Oct 27 2020

Bibliographical note

KAUST Repository Item: Exported on 2020-10-29
Acknowledged KAUST grant number(s): OSR-CRG2017-3434
Acknowledgements: The authors would like to thank the Editor, Associate Editor and a referee for valuable suggestions that have improved the manuscript. The data that support the findings of this study are openly available from the European Climate Assessment & Dataset project at This publication is based upon work supported by the King AbdullahUniversity of Science and Technology (KAUST) Office of Sponsored Research (OSR) underAward No. OSR-CRG2017-3434.


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