arXiv subjects

Raphaël Huser

Publications and source records attributed to Raphaël Huser.

72 records · Page 4Linked to original sources

arXiv2020

Advances in Statistical Modeling of Spatial Extremes

The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or $r$-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often suggests that such asymptotic models are too rigidly constrained, and that they do not adequately capture the frequent situation where more severe events tend to be spatially more localized. In other words, these asymptotic models have a strong tail dependence that persists at increasingly high levels, while data usually suggest that it should weaken instead. Another well-known limitation of classical spatial extremes models is that they are either computationally prohibitive to fit in high dimensions, or they need to be fitted using less efficient techniques. In this review paper, we describe recent progress in the modeling and inference for spatial extremes, focusing on new models that have more flexible tail structures that can bridge asymptotic dependence classes, and that are more easily amenable to likelihood-based inference for large datasets. In particular, we discuss various types of random scale constructions, as well as the conditional spatial extremes model, which have recently been getting increasing attention within the statistics of extremes community. We illustrate some of these new spatial models on two different environmental applications.

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arXiv2020

Spatial hierarchical modeling of threshold exceedances using rate mixtures

We develop new flexible 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 flexibility. 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.

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arXiv2020

Modeling Non-Stationary Temperature Maxima Based on Extremal Dependence Changing with Event Magnitude

The modeling of spatio-temporal trends in temperature extremes can help better understand the structure and frequency of heatwaves in a changing climate. Here, we study annual temperature maxima over Southern Europe using a century-spanning dataset observed at 44 monitoring stations. Extending the spectral representation of max-stable processes, our modeling framework relies on a novel construction of max-infinitely divisible processes, which include covariates to capture spatio-temporal non-stationarities. Our new model keeps a popular max-stable process on the boundary of the parameter space, while flexibly capturing weakening extremal dependence at increasing quantile levels and asymptotic independence. This is achieved by linking the overall magnitude of a spatial event to its spatial correlation range, in such a way that more extreme events become less spatially dependent, thus more localized. Our model reveals salient features of the spatio-temporal variability of European temperature extremes, and it clearly outperforms natural alternative models. Results show that the spatial extent of heatwaves is smaller for more severe events at higher altitudes, and that recent heatwaves are moderately wider. Our probabilistic assessment of the 2019 annual maxima confirms the severity of the 2019 heatwaves both spatially and at individual sites, especially when compared to climatic conditions prevailing in 1950-1975.

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arXiv2020

High-resolution Bayesian mapping of landslide hazard with unobserved trigger event

Statistical models for landslide hazard enable mapping of risk factors and landslide occurrence intensity by using geomorphological covariates available at high spatial resolution. However, the spatial distribution of the triggering event (e.g., precipitation or earthquakes) is often not directly observed. In this paper, we develop Bayesian spatial hierarchical models for point patterns of landslide occurrences using different types of log-Gaussian Cox processes. Starting from a competitive baseline model that captures the unobserved precipitation trigger through a spatial random effect at slope unit resolution, we explore novel complex model structures that take clusters of events arising at small spatial scales into account, as well as nonlinear or spatially-varying covariate effects. For a 2009 event of around 4000 precipitation-triggered landslides in Sicily, Italy, we show how to fit our proposed models efficiently using the integrated nested Laplace approximation (INLA), and rigorously compare the performance of our models both from a statistical and applied perspective. In this context, we argue that model comparison should not be based on a single criterion, and that different models of various complexity may provide insights into complementary aspects of the same applied problem. In our application, our models are found to have mostly the same spatial predictive performance, implying that key to successful prediction is the inclusion of a slope-unit resolved random effect capturing the precipitation trigger. Interestingly, a parsimonious formulation of space-varying slope effects reflects a physical interpretation of the precipitation trigger: in subareas with weak trigger, the slope steepness is shown to be mostly irrelevant.

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arXiv2020

A Hierarchical Max-Infinitely Divisible Spatial Model for Extreme Precipitation

Understanding the spatial extent of extreme precipitation is necessary for determining flood risk and adequately designing infrastructure (e.g., stormwater pipes) to withstand such hazards. While environmental phenomena typically exhibit weakening spatial dependence at increasingly extreme levels, limiting max-stable process models for block maxima have a rigid dependence structure that does not capture this type of behavior. We propose a flexible Bayesian model from a broader family of (conditionally) max-infinitely divisible processes that allows for weakening spatial dependence at increasingly extreme levels, and due to a hierarchical representation of the likelihood in terms of random effects, our inference approach scales to large datasets. Therefore, our model not only has a flexible dependence structure, but it also allows for fast, fully Bayesian inference, prediction and conditional simulation in high dimensions. The proposed model is constructed using flexible random basis functions that are estimated from the data, allowing for straightforward inspection of the predominant spatial patterns of extremes. In addition, the described process possesses (conditional) max-stability as a special case, making inference on the tail dependence class possible. We apply our model to extreme precipitation in North-Eastern America, and show that the proposed model adequately captures the extremal behavior of the data. Interestingly, we find that the principal modes of spatial variation estimated from our model resemble observed patterns in extreme precipitation events occurring along the coast (e.g., with localized tropical cyclones and convective storms) and mountain range borders. Our model, which can easily be adapted to other types of environmental datasets, is therefore useful to identify extreme weather patterns and regions at risk.

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arXiv2020

Max-and-Smooth: a two-step approach for approximate Bayesian inference in latent Gaussian models

With modern high-dimensional data, complex statistical models are necessary, requiring computationally feasible inference schemes. We introduce Max-and-Smooth, an approximate Bayesian inference scheme for a flexible class of latent Gaussian models (LGMs) where one or more of the likelihood parameters are modeled by latent additive Gaussian processes. Max-and-Smooth consists of two-steps. In the first step (Max), the likelihood function is approximated by a Gaussian density with mean and covariance equal to either (a) the maximum likelihood estimate and the inverse observed information, respectively, or (b) the mean and covariance of the normalized likelihood function. In the second step (Smooth), the latent parameters and hyperparameters are inferred and smoothed with the approximated likelihood function. The proposed method ensures that the uncertainty from the first step is correctly propagated to the second step. Since the approximated likelihood function is Gaussian, the approximate posterior density of the latent parameters of the LGM (conditional on the hyperparameters) is also Gaussian, thus facilitating efficient posterior inference in high dimensions. Furthermore, the approximate marginal posterior distribution of the hyperparameters is tractable, and as a result, the hyperparameters can be sampled independently of the latent parameters. In the case of a large number of independent data replicates, sparse precision matrices, and high-dimensional latent vectors, the speedup is substantial in comparison to an MCMC scheme that infers the posterior density from the exact likelihood function. The proposed inference scheme is demonstrated on one spatially referenced real dataset and on simulated data mimicking spatial, temporal, and spatio-temporal inference problems. Our results show that Max-and-Smooth is accurate and fast.

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arXiv2019

Space-Time Landslide Predictive Modelling

Landslides are nearly ubiquitous phenomena and pose severe threats to people, properties, and the environment. Investigators have for long attempted to estimate landslide hazard to determine where, when, and how destructive landslides are expected to be in an area. This information is useful to design landslide mitigation strategies, and to reduce landslide risk and societal and economic losses. In the geomorphology literature, most attempts at predicting the occurrence of populations of landslides rely on the observation that landslides are the result of multiple interacting, conditioning and triggering factors. Here, we propose a novel Bayesian modelling framework for the prediction of space-time landslide occurrences of the slide type caused by weather triggers. We consider log-Gaussian cox processes, assuming that individual landslides stem from a point process described by an unknown intensity function. We tested our prediction framework in the Collazzone area, Umbria, Central Italy, for which a detailed multi-temporal landslide inventory spanning 1941-2014 is available together with lithological and bedding data. We tested five models of increasing complexity. Our most complex model includes fixed effects and latent spatio-temporal effects, thus largely fulfilling the common definition of landslide hazard in the literature. We quantified the spatio-temporal predictive skill of our model and found that it performed better than simpler alternatives. We then developed a novel classification strategy and prepared an intensity-susceptibility landslide map, providing more information than traditional susceptibility zonations for land planning and management. We expect our novel approach to lead to better projections of future landslides, and to improve our collective understanding of the evolution of landscapes dominated by mass-wasting processes under geophysical and weather triggers.

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arXiv2019

Editorial: EVA 2019 data competition on spatio-temporal prediction of Red Sea surface temperature extremes

Large, non-stationary spatio-temporal data are ubiquitous in modern statistical applications, and the modeling of spatio-temporal extremes is crucial for assessing risks in environmental sciences among others. While the modeling of extremes is challenging in itself, the prediction of rare events at unobserved spatial locations and time points is even more difficult. In this editorial, we describe the data competition that was organized for the 11th international conference on Extreme-Value Analysis (EVA 2019), for which several teams modeled and predicted Red Sea surface temperature extremes over space and time. After introducing the dataset and the goal of the competition, we disclose the final ranking of the teams, and we finally discuss some interesting outcomes and future challenges.

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arXiv2019

A spliced Gamma-Generalized Pareto model for short-term extreme wind speed probabilistic forecasting

Renewable sources of energy such as wind power have become a sustainable alternative to fossil fuel-based energy. However, the uncertainty and fluctuation of the wind speed derived from its intermittent nature bring a great threat to the wind power production stability, and to the wind turbines themselves. Lately, much work has been done on developing models to forecast average wind speed values, yet surprisingly little has focused on proposing models to accurately forecast extreme wind speeds, which can damage the turbines. In this work, we develop a flexible spliced Gamma-Generalized Pareto model to forecast extreme and non-extreme wind speeds simultaneously. Our model belongs to the class of latent Gaussian models, for which inference is conveniently performed based on the integrated nested Laplace approximation method. Considering a flexible additive regression structure, we propose two models for the latent linear predictor to capture the spatio-temporal dynamics of wind speeds. Our models are fast to fit and can describe both the bulk and the tail of the wind speed distribution while producing short-term extreme and non-extreme wind speed probabilistic forecasts.

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arXiv2019

Local likelihood estimation of complex tail dependence structures, applied to U.S. precipitation extremes

To disentangle the complex non-stationary dependence structure of precipitation extremes over the entire contiguous U.S., we propose a flexible local approach based on factor copula models. Our sub-asymptotic spatial modeling framework yields non-trivial tail dependence structures, with a weakening dependence strength as events become more extreme, a feature commonly observed with precipitation data but not accounted for in classical asymptotic extreme-value models. To estimate the local extremal behavior, we fit the proposed model in small regional neighborhoods to high threshold exceedances, under the assumption of local stationarity, which allows us to gain in flexibility. Adopting a local censored likelihood approach, inference is made on a fine spatial grid, and local estimation is performed by taking advantage of distributed computing resources and the embarrassingly parallel nature of this estimation procedure. The local model is efficiently fitted at all grid points, and uncertainty is measured using a block bootstrap procedure. An extensive simulation study shows that our approach can adequately capture complex, non-stationary dependencies, while our study of U.S. winter precipitation data reveals interesting differences in local tail structures over space, which has important implications on regional risk assessment of extreme precipitation events.

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arXiv2018

Bayesian model averaging over tree-based dependence structures for multivariate extremes

Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical dependence structure of the max-stable nested logistic distribution and that identifies possible clusters of extreme variables using reversible jump Markov chain Monte Carlo techniques. Parsimonious representations are achieved when clusters of extreme variables are found to be completely independent. Moreover, we significantly decrease the computational complexity of full likelihood inference by deriving a recursive formula for the nested logistic model likelihood. The algorithm performance is verified through extensive simulation experiments which also compare different likelihood procedures. The new methodology is used to investigate the dependence relationships between extreme concentration of multiple pollutants in California and how these pollutants are related to extreme weather conditions. Overall, we show that our approach allows for the representation of complex extremal dependence structures and has valid applications in multivariate data analysis, such as air pollution monitoring, where it can guide policymaking.

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arXiv2018

Full likelihood inference for max-stable data

We show how to perform full likelihood inference for max-stable multivariate distributions or processes based on a stochastic Expectation-Maximisation algorithm, which combines statistical and computational efficiency in high-dimensions. The good performance of this methodology is demonstrated by simulation based on the popular logistic and Brown--Resnick models, and it is shown to provide dramatic computational time improvements with respect to a direct computation of the likelihood. Strategies to further reduce the computational burden are also discussed.

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arXiv2018

Bayesian Modeling of Air Pollution Extremes Using Nested Multivariate Max-Stable Processes

Capturing the potentially strong dependence among the peak concentrations of multiple air pollutants across a spatial region is crucial for assessing the related public health risks. In order to investigate the multivariate spatial dependence properties of air pollution extremes, we introduce a new class of multivariate max-stable processes. Our proposed model admits a hierarchical tree-based formulation, in which the data are conditionally independent given some latent nested $α$-stable random factors. The hierarchical structure facilitates Bayesian inference and offers a convenient and interpretable characterization. We fit this nested multivariate max-stable model to the maxima of air pollution concentrations and temperatures recorded at a number of sites in the Los Angeles area, showing that the proposed model succeeds in capturing their complex tail dependence structure.

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arXiv2018

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

This work has been motivated by the challenge of the 2017 conference on Extreme-Value Analysis (EVA2017), with the goal of predicting daily precipitation quantiles at the $99.8\%$ level for each month at observed and unobserved locations. We here develop a Bayesian generalized additive modeling framework tailored to estimate complex trends in marginal extremes observed over space and time. Our approach is based on a set of regression equations linked to the exceedance probability above a high threshold and to the size of the excess, the latter being modeled using the generalized Pareto (GP) distribution suggested by Extreme-Value Theory. Latent random effects are modeled additively and semi-parametrically using Gaussian process priors, which provides high flexibility and interpretability. Fast and accurate estimation of posterior distributions may be performed thanks to the Integrated Nested Laplace approximation (INLA), efficiently implemented in the R-INLA software, which we also use for determining a nonstationary threshold based on a model for the body of the distribution. We show that the GP distribution meets the theoretical requirements of INLA, and we then develop a penalized complexity prior specification for the tail index, which is a crucial parameter for extrapolating tail event probabilities. This prior concentrates mass close to a light exponential tail while allowing heavier tails by penalizing the distance to the exponential distribution. We illustrate this methodology through the modeling of spatial and seasonal trends in daily precipitation data provided by the EVA2017 challenge. Capitalizing on R-INLA's fast computation capacities and large distributed computing resources, we conduct an extensive cross-validation study to select model parameters governing the smoothness of trends. Our results outperform simple benchmarks and are comparable to the best-scoring approach.

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arXiv2017

Modeling soil organic carbon with Quantile Regression: Dissecting predictors' effects on carbon stocks

Soil Organic Carbon (SOC) estimation is crucial to manage both natural and anthropic ecosystems and has recently been put under the magnifying glass after the Paris agreement 2016 due to its relationship with greenhouse gas. Statistical applications have dominated the SOC stock mapping at regional scale so far. However, the community has hardly ever attempted to implement Quantile Regression (QR) to spatially predict the SOC distribution. In this contribution, we test QR to estimate SOC stock (0-30 $cm$ depth) in the agricultural areas of a highly variable semi-arid region (Sicily, Italy, around 25,000 $km2$) by using topographic and remotely sensed predictors. We also compare the results with those from available SOC stock measurement. The QR models produced robust performances and allowed to recognize dominant effects among the predictors with respect to the considered quantile. This information, currently lacking, suggests that QR can discern predictor influences on SOC stock at specific sub-domains of each predictors. In this work, the predictive map generated at the median shows lower errors than those of the Joint Research Centre and International Soil Reference, and Information Centre benchmarks. The results suggest the use of QR as a comprehensive and effective method to map SOC using legacy data in agro-ecosystems. The R code scripted in this study for QR is included.

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arXiv2015

High-order Composite Likelihood Inference for Max-Stable Distributions and Processes

In multivariate or spatial extremes, inference for max-stable processes observed at a large collection of locations is among the most challenging problems in computational statistics, and current approaches typically rely on less expensive composite likelihoods constructed from small subsets of data. In this work, we explore the limits of modern state-of-the-art computational facilities to perform full likelihood inference and to efficiently evaluate high-order composite likelihoods. With extensive simulations, we assess the loss of information of composite likelihood estimators with respect to a full likelihood approach for some widely-used multivariate or spatial extreme models, we discuss how to choose composite likelihood truncation to improve the efficiency, and we also provide recommendations for practitioners.

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arXiv2015

Likelihood estimators for multivariate extremes

The main approach to inference for multivariate extremes consists in approximating the joint upper tail of the observations by a parametric family arising in the limit for extreme events. The latter may be expressed in terms of componentwise maxima, high threshold exceedances or point processes, yielding different but related asymptotic characterizations and estimators. The present paper clarifies the connections between the main likelihood estimators, and assesses their practical performance. We investigate their ability to estimate the extremal dependence structure and to predict future extremes, using exact calculations and simulation, in the case of the logistic model.

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arXiv2012

Space-time modelling of extreme events

Max-stable processes are the natural analogues of the generalized extreme-value distribution for the modelling of extreme events in space and time. Under suitable conditions, these processes are asymptotically justified models for maxima of independent replications of random fields, and they are also suitable for the modelling of joint individual extreme measurements over high thresholds. This paper extends a model of Schlather (2001) to the space-time framework, and shows how a pairwise censored likelihood can be used for consistent estimation under mild mixing conditions. Estimator efficiency is also assessed and the choice of pairs to be included in the pairwise likelihood is discussed based on computations for simple time series models. The ideas are illustrated by an application to hourly precipitation data over Switzerland.

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