Thomas Opitz

Efficient inference and simulation for elliptical Pareto processes

Recent advances in extreme value theory have established

Modeling asymptotically independent spatial extremes based on Laplace random fields

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Point process-based modeling of multiple debris flow landslides using INLA: an application to the 2009 Messina disaster

-Pareto processes as the natural limits for extreme events defined in terms of exceedances of a risk functional. In this paper we provide methods for the practical modelling of data based on a tractable yet flexible dependence model. We introduce the class of elliptical

Index for Predicting Insurance Claims from Wind Storms with an Application in France

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INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles

-Pareto processes, which arise as the limits of threshold exceedances of certain elliptical processes characterized by a correlation function and a shape parameter. An efficient inference method based on maximizing a full likelihood with partial censoring is developed. Novel procedures for exact conditional and unconditional simulation are proposed. These ideas are illustrated using precipitation extremes in Switzerland.

Bridging asymptotic independence and dependence in spatial extremes using Gaussian scale mixtures

We tackle the modeling of threshold exceedances in asymptotically independent stochastic processes by constructions based on Laplace random fields. These are defined as Gaussian random fields scaled with a stochastic variable following an exponential distribution. This framework yields useful asymptotic properties while remaining statistically convenient. Univariate distribution tails are of the half exponential type and are part of the limiting generalized Pareto distributions for threshold exceedances. After normalizing marginal tail distributions in data, a standard Laplace field can be used to capture spatial dependence among extremes. Asymptotic properties of Laplace fields are explored and compared to the classical framework of asymptotic dependence. Multivariate joint tail decay rates for Laplace fields are slower than for Gaussian fields with the same covariance structure; hence they provide more conservative estimates of very extreme joint risks while maintaining asymptotic independence. Statistical inference is illustrated on extreme wind gusts in the Netherlands where a comparison to the Gaussian dependence model shows a better goodness-of-fit in terms of Akaikes criterion. In this specific application we fit the well-adapted Weibull distribution as univariate tail model, such that the normalization of univariate tail distributions can be done through a simple power transformation of data.

Wind storm risk management: sensitivity of return period calculations and spread on the territory

AbstractWe develop a stochastic modeling approach based on spatial point processes of log-Gaussian Cox type for a collection of around 5000 landslide events provoked by a precipitation trigger in Sicily, Italy. Through the embedding into a hierarchical Bayesian estimation framework, we can use the integrated nested Laplace approximation methodology to make inference and obtain the posterior estimates of spatially distributed covariate and random effects. Several mapping units are useful to partition a given study area in landslide prediction studies. These units hierarchically subdivide the geographic space from the highest grid-based resolution to the stronger morphodynamic-oriented slope units. Here we integrate both mapping units into a single hierarchical model, by treating the landslide triggering locations as a random point pattern. This approach diverges fundamentally from the unanimously used presence–absence structure for areal units since we focus on modeling the expected landslide count jointly within the two mapping units. Predicting this landslide intensity provides more detailed and complete information as compared to the classically used susceptibility mapping approach based on relative probabilities. To illustrate the model’s versatility, we compute absolute probability maps of landslide occurrences and check their predictive power over space. While the landslide community typically produces spatial predictive models for landslides only in the sense that covariates are spatially distributed, no actual spatial dependence has been explicitly integrated so far. Our novel approach features a spatial latent effect defined at the slope unit level, allowing us to assess the spatial influence that remains unexplained by the covariates in the model. For rainfall-induced landslides in regions where the raingauge network is not sufficient to capture the spatial distribution of the triggering precipitation event, this latent effect provides valuable imaging support on the unobserved rainfall pattern.

Penultimate modeling of spatial extremes: statistical inference for max-infinitely divisible processes

For insurance companies, wind storms represent a main source of volatility, leading to potentially huge aggregated claim amounts. In this article, we compare different constructions of a storm index allowing us to assess the economic impact of storms on an insurance portfolio by exploiting information from historical wind speed data. Contrary to historical insurance portfolio data, meteorological variables show fewer nonstationarities between years and are easily available with long observation records; hence, they represent a valuable source of additional information for insurers if the relation between observations of claims and wind speeds can be revealed. Since standard correlation measures between raw wind speeds and insurance claims are weak, a storm index focusing on high wind speeds can afford better information. A storm index approach has been applied to yearly aggregated claim amounts in Germany with promising results. Using historical meteorological and insurance data, we assess the consistency of the proposed index constructions with respect to various parameters and weights. Moreover, we are able to place the major insurance events since 1998 on a broader horizon beyond 40 years. Our approach provides a meteorological justification for calculating the return periods of extreme-storm-related insurance events whose magnitude has rarely been reached.

Exceedance-based nonlinear regression of tail dependence

This work is motivated by the challenge organized for the 10th International Conference on Extreme-Value Analysis (EVA2017) to predict daily precipitation quantiles at the 99.8%

Wind Storm Risk Management

99.8\%