arXiv subjects

Raphaël Huser

Publications and source records attributed to Raphaël Huser.

At least 55 records · Page 3Linked to original sources

arXiv2022

An Efficient Workflow for Modelling High-Dimensional Spatial Extremes

A successful model for high-dimensional spatial extremes should, in principle, be able to describe both weakening extremal dependence at increasing levels and changes in the type of extremal dependence class as a function of the distance between locations. Furthermore, the model should allow for computationally tractable inference using inference methods that efficiently extract information from data and that are robust to model misspecification. In this paper, we demonstrate how to fulfil all these requirements by developing a comprehensive methodological workflow for efficient Bayesian modelling of high-dimensional spatial extremes using the spatial conditional extremes model while performing fast inference with R-INLA. We then propose a post hoc adjustment method that results in more robust inference by properly accounting for possible model misspecification. The developed methodology is applied for modelling extreme hourly precipitation from high-resolution radar data in Norway. Inference is computationally efficient, and the resulting model fit successfully captures the main trends in the extremal dependence structure of the data. Robustifying the model fit by adjusting for possible misspecification further improves model performance.

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arXiv2022

Spatial modeling and future projection of extreme precipitation extents

Extreme precipitation events with large spatial extents may have more severe impacts than localized events as they can lead to widespread flooding. It is debated how climate change may affect the spatial extent of precipitation extremes, whose investigation often directly relies on simulations from climate models. Here, we use a different strategy to investigate how future changes in spatial extents of precipitation extremes differ across climate zones and seasons in two river basins (Danube and Mississippi). We rely on observed precipitation extremes while exploiting a physics-based mean temperature covariate, which enables us to project future precipitation extents. We include the covariate into newly developed time-varying $r$-Pareto processes using a suitably chosen spatial aggregation functional $r$. This model captures temporal non-stationarity in the spatial dependence structure of precipitation extremes by linking it to the temperature covariate, which we derive from observations for model calibration and from debiased climate simulations (CMIP6) for projections. For both river basins, our results show negative correlation between the spatial extent and the temperature covariate for most of the rain season and an increasing trend in the margins, indicating a decrease in spatial precipitation extent in a warming climate during rain seasons as precipitation intensity increases locally.

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arXiv2022

Partial Tail-Correlation Coefficient Applied to Extremal-Network Learning

We propose a novel extremal dependence measure called the partial tail-correlation coefficient (PTCC), in analogy to the partial correlation coefficient in classical multivariate analysis. The construction of our new coefficient is based on the framework of multivariate regular variation and transformed-linear algebra operations. We show how this coefficient allows identifying pairs of variables that have partially uncorrelated tails given the other variables in a random vector. Unlike other recently introduced conditional independence frameworks for extremes, our approach requires minimal modeling assumptions and can thus be used in exploratory analyses to learn the structure of extremal graphical models. Similarly to traditional Gaussian graphical models where edges correspond to the non-zero entries of the precision matrix, we can exploit classical inference methods for high-dimensional data, such as the graphical LASSO with Laplacian spectral constraints, to efficiently learn the extremal network structure via the PTCC. We apply our new method to study extreme risk networks in two different datasets (extreme river discharges and historical global currency exchange data) and show that we can extract meaningful extremal structures with meaningful domain-specific interpretations.

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arXiv2022

Flexible Modeling of Multivariate Spatial Extremes

We develop a novel multi-factor copula model for multivariate spatial extremes, which is designed to capture the different combinations of marginal and cross-extremal dependence structures within and across different spatial random fields. Our proposed model, which can be seen as a multi-factor copula model, can capture all possible distinct combinations of extremal dependence structures within each individual spatial process while allowing flexible cross-process extremal dependence structures for both upper and lower tails. We show how to perform Bayesian inference for the proposed model using a Markov chain Monte Carlo algorithm based on carefully designed block proposals with an adaptive step size. In our real data application, we apply our model to study the upper and lower extremal dependence structures of the daily maximum air temperature (TMAX) and daily minimum air temperature (TMIN) from the state of Alabama in the southeastern United States. The fitted multivariate spatial model is found to provide a good fit in the lower and upper joint tails, both in terms of the spatial dependence structure within each individual process, as well as in terms of the cross-process dependence structure. Our results suggest that the TMAX and TMIN processes are quite strongly spatially dependent over the state of Alabama, and moderately cross-dependent. From a practical perspective, this implies that it may be worthwhile to model them jointly when interest lies in a computing spatial risk measures that involve both quantities.

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arXiv2022

Modeling spatial tail dependence with Cauchy convolution processes

We study the class of dependence models for spatial data obtained from Cauchy convolution processes based on different types of kernel functions. We show that the resulting spatial processes have appealing tail dependence properties, such as tail dependence at short distances and independence at long distances with suitable kernel functions. We derive the extreme-value limits of these processes, study their smoothness properties, and detail some interesting special cases. To get higher flexibility at sub-asymptotic levels and separately control the bulk and the tail dependence properties, we further propose spatial models constructed by mixing a Cauchy convolution process with a Gaussian process. We demonstrate that this framework indeed provides a rich class of models for the joint modeling of the bulk and the tail behaviors. Our proposed inference approach relies on matching model-based and empirical summary statistics, and an extensive simulation study shows that it yields accurate estimates. We demonstrate our new methodology by application to a temperature dataset measured at 97 monitoring stations in the state of Oklahoma, US. Our results indicate that our proposed model provides a very good fit to the data, and that it captures both the bulk and the tail dependence structures accurately.

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arXiv2022

Joint modeling of landslide counts and sizes using spatial marked point processes with sub-asymptotic mark distributions

To accurately quantify landslide hazard in a region of Turkey, we develop new marked point process models within a Bayesian hierarchical framework for the joint prediction of landslide counts and sizes. To accommodate for the dominant role of the few largest landslides in aggregated sizes, we leverage mark distributions with strong justification from extreme-value theory, thus bridging the two broad areas of statistics of extremes and marked point patterns. At the data level, we assume a Poisson distribution for landslide counts, while we compare different "sub-asymptotic" distributions for landslide sizes to flexibly model their upper and lower tails. At the latent level, Poisson intensities and the median of the size distribution vary spatially in terms of fixed and random effects, with shared spatial components capturing cross-correlation between landslide counts and sizes. We robustly model spatial dependence using intrinsic conditional autoregressive priors. Our novel models are fitted efficiently using a customized adaptive Markov chain Monte Carlo algorithm. We show that, for our dataset, sub-asymptotic mark distributions provide improved predictions of large landslide sizes compared to more traditional choices. To showcase the benefits of joint occurrence-size models and illustrate their usefulness for risk assessment, we map landslide hazard along major roads.

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arXiv2022

Practical strategies for GEV-based regression models for extremes

The generalised extreme value (GEV) distribution is a three parameter family that describes the asymptotic behaviour of properly renormalised maxima of a sequence of independent and identically distributed random variables. If the shape parameter $ξ$ is zero, the GEV distribution has unbounded support, whereas if $ξ$ is positive, the limiting distribution is heavy-tailed with infinite upper endpoint but finite lower endpoint. In practical applications, we assume that the GEV family is a reasonable approximation for the distribution of maxima over blocks, and we fit it accordingly. This implies that GEV properties, such as finite lower endpoint in the case $ξ>0$, are inherited by the finite-sample maxima, which might not have bounded support. This is particularly problematic when predicting extreme observations based on multiple and interacting covariates. To tackle this usually overlooked issue, we propose a blended GEV distribution, which smoothly combines the left tail of a Gumbel distribution (GEV with $ξ=0$) with the right tail of a Fréchet distribution (GEV with $ξ>0$) and, therefore, has unbounded support. Using a Bayesian framework, we reparametrise the GEV distribution to offer a more natural interpretation of the (possibly covariate-dependent) model parameters. Independent priors over the new location and spread parameters induce a joint prior distribution for the original location and scale parameters. We introduce the concept of property-preserving penalised complexity (P$^3$C) priors and apply it to the shape parameter to preserve first and second moments. We illustrate our methods with an application to NO$_2$ pollution levels in California, which reveals the robustness of the bGEV distribution, as well as the suitability of the new parametrisation and the P$^3$C prior framework.

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arXiv2022

Vecchia Likelihood Approximation for Accurate and Fast Inference in Intractable Spatial Extremes Models

Max-stable processes are the most popular models for high-impact spatial extreme events, as they arise as the only possible limits of spatially-indexed block maxima. However, likelihood inference for such models suffers severely from the curse of dimensionality, since the likelihood function involves a combinatorially exploding number of terms. In this paper, we propose using the Vecchia approximation, which conveniently decomposes the full joint density into a linear number of low-dimensional conditional density terms based on well-chosen conditioning sets designed to improve and accelerate inference in high dimensions. Theoretical asymptotic relative efficiencies in the Gaussian setting and simulation experiments in the max-stable setting show significant efficiency gains and computational savings using the Vecchia likelihood approximation method compared to traditional composite likelihoods. Our application to extreme sea surface temperature data at more than a thousand sites across the entire Red Sea further demonstrates the superiority of the Vecchia likelihood approximation for fitting complex models with intractable likelihoods, delivering significantly better results than traditional composite likelihoods, and accurately capturing the extremal dependence structure at lower computational cost.

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arXiv2022

Exact Simulation of Max-Infinitely Divisible Processes

Max-infinitely divisible (max-id) processes play a central role in extreme-value theory and include the subclass of all max-stable processes. They allow for a constructive representation based on the pointwise maximum of random functions drawn from a Poisson point process defined on a suitable function space. Simulating from a max-id process is often difficult due to its complex stochastic structure, while calculating its joint density in high dimensions is often numerically infeasible. Therefore, exact and efficient simulation techniques for max-id processes are useful tools for studying the characteristics of the process and for drawing statistical inferences. Inspired by the simulation algorithms for max-stable processes, theory and algorithms to generalize simulation approaches tailored for certain flexible (existing or new) classes of max-id processes are presented. Efficient simulation for a large class of models can be achieved by implementing an adaptive rejection sampling scheme to sidestep a numerical integration step in the algorithm. The results of a simulation study highlight that our simulation algorithm works as expected and is highly accurate and efficient, such that it clearly outperforms customary approximate sampling schemes. As a by-product, new max-id models, which can be represented as pointwise maxima of general location-scale mixtures and possess flexible tail dependence structures capturing a wide range of asymptotic dependence scenarios, are also developed.

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arXiv2022

Joint Modeling and Prediction of Massive Spatio-Temporal Wildfire Count and Burnt Area Data with the INLA-SPDE Approach

This paper describes the methodology used by the team RedSea in the data competition organized for EVA 2021 conference. We develop a novel two-part model to jointly describe the wildfire count data and burnt area data provided by the competition organizers with covariates. Our proposed methodology relies on the integrated nested Laplace approximation combined with the stochastic partial differential equation (INLA-SPDE) approach. In the first part, a binary non-stationary spatio-temporal model is used to describe the underlying process that determines whether or not there is wildfire at a specific time and location. In the second part, we consider a non-stationary model that is based on log-Gaussian Cox processes for positive wildfire count data, and a non-stationary log-Gaussian model for positive burnt area data. Dependence between the positive count data and positive burnt area data is captured by a shared spatio-temporal random effect. Our two-part modeling approach performs well in terms of the prediction score criterion chosen by the data competition organizers. Moreover, our model results show that surface pressure is the most influential driver for the occurrence of a wildfire, whilst surface net solar radiation and surface pressure are the key drivers for large numbers of wildfires, and temperature and evaporation are the key drivers of large burnt areas.

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arXiv2021

A flexible Bayesian hierarchical modeling framework for spatially dependent peaks-over-threshold data

In this work, we develop a constructive modeling framework for extreme threshold exceedances in repeated observations of spatial fields, based on general product mixtures of random fields possessing light or heavy-tailed margins and various spatial dependence characteristics, which are suitably designed to provide high flexibility in the tail and at sub-asymptotic levels. Our proposed model is akin to a recently proposed Gamma-Gamma model using a ratio of processes with Gamma marginal distributions, but it possesses a higher degree of flexibility in its joint tail structure, capturing strong dependence more easily. We focus on constructions with the following three product factors, whose different roles ensure their statistical identifiability: a heavy-tailed spatially-dependent field, a lighter-tailed spatially-constant field, and another lighter-tailed spatially-independent field. Thanks to the model's hierarchical formulation, inference may be conveniently performed based on Markov chain Monte Carlo methods. We leverage the Metropolis adjusted Langevin algorithm (MALA) with random block proposals for latent variables, as well as the stochastic gradient Langevin dynamics (SGLD) algorithm for hyperparameters, in order to fit our proposed model very efficiently in relatively high spatio-temporal dimensions, while simultaneously censoring non-threshold exceedances and performing spatial prediction at multiple sites. The censoring mechanism is applied to the spatially independent component, such that only univariate cumulative distribution functions have to be evaluated. We explore the theoretical properties of the novel model, and illustrate the proposed methodology by simulation and application to daily precipitation data from North-Eastern Spain measured at about 100 stations over the period 2011-2020.

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arXiv2021

Latent Gaussian Models for High-Dimensional Spatial Extremes

In this chapter, we show how to efficiently model high-dimensional extreme peaks-over-threshold events over space in complex non-stationary settings, using extended latent Gaussian Models (LGMs), and how to exploit the fitted model in practice for the computation of long-term return levels. The extended LGM framework assumes that the data follow a specific parametric distribution, whose unknown parameters are transformed using a multivariate link function and are then further modeled at the latent level in terms of fixed and random effects that have a joint Gaussian distribution. In the extremal context, we here assume that the data level distribution is described in terms of a Poisson point process likelihood, motivated by asymptotic extreme-value theory, and which conveniently exploits information from all threshold exceedances. This contrasts with the more common data-wasteful approach based on block maxima, which are typically modeled with the generalized extreme-value (GEV) distribution. When conditional independence can be assumed at the data level and latent random effects have a sparse probabilistic structure, fast approximate Bayesian inference becomes possible in very high dimensions, and we here present the recently proposed inference approach called "Max-and-Smooth", which provides exceptional speed-up compared to alternative methods. The proposed methodology is illustrated by application to satellite-derived precipitation data over Saudi Arabia, obtained from the Tropical Rainfall Measuring Mission, with 2738 grid cells and about 20 million spatio-temporal observations in total. Our fitted model captures the spatial variability of extreme precipitation satisfactorily and our results show that the most intense precipitation events are expected near the south-western part of Saudi Arabia, along the Red Sea coastline.

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arXiv2021

Modeling spatial extremes using normal mean-variance mixtures

Classical models for multivariate or spatial extremes are mainly based upon the asymptotically justified max-stable or generalized Pareto processes. These models are suitable when asymptotic dependence is present, i.e., the joint tail decays at the same rate as the marginal tail. However, recent environmental data applications suggest that asymptotic independence is equally important and, unfortunately, existing spatial models in this setting that are both flexible and can be fitted efficiently are scarce. Here, we propose a new spatial copula model based on the generalized hyperbolic distribution, which is a specific normal mean-variance mixture and is very popular in financial modeling. The tail properties of this distribution have been studied in the literature, but with contradictory results. It turns out that the proofs from the literature contain mistakes. We here give a corrected theoretical description of its tail dependence structure and then exploit the model to analyze a simulated dataset from the inverted Brown-Resnick process, hindcast significant wave height data in the North Sea, and wind gust data in the state of Oklahoma, USA. We demonstrate that our proposed model is flexible enough to capture the dependence structure not only in the tail but also in the bulk.

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arXiv2021

Asymmetric tail dependence modeling, with application to cryptocurrency market data

Since the inception of Bitcoin in 2008, cryptocurrencies have played an increasing role in the world of e-commerce, but the recent turbulence in the cryptocurrency market in 2018 has raised some concerns about their stability and associated risks. For investors, it is crucial to uncover the dependence relationships between cryptocurrencies for a more resilient portfolio diversification. Moreover, the stochastic behavior in both tails is important, as long positions are sensitive to a decrease in prices (lower tail), while short positions are sensitive to an increase in prices (upper tail). In order to assess both risk types, we develop in this paper a flexible copula model which is able to distinctively capture asymptotic dependence or independence in its lower and upper tails simultaneously. Our proposed model is parsimonious and smoothly bridges (in each tail) both extremal dependence classes in the interior of the parameter space. Inference is performed using a full or censored likelihood approach, and we investigate by simulation the estimators' efficiency under three different censoring schemes which reduce the impact of non-extreme observations. We also develop a local likelihood approach to capture the temporal dynamics of extremal dependence among two leading cryptocurrencies. We here apply our model to historical closing prices of five leading cryotocurrencies, which share most of the cryptocurrency market capitalizations. The results show that our proposed copula model outperforms alternative copula models and that the lower tail dependence level between most pairs of leading cryptocurrencies -- and in particular Bitcoin and Ethereum -- has become stronger over time, smoothly transitioning from an asymptotic independence regime to an asymptotic dependence regime in recent years, whilst the upper tail has been relatively more stable overall at a weaker dependence level.

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arXiv2021

Approximate Bayesian inference for analysis of spatio-temporal flood frequency data

Extreme floods cause casualties, and widespread damage to property and vital civil infrastructure. We here propose a Bayesian approach for predicting extreme floods using the generalized extreme-value (GEV) distribution within gauged and ungauged catchments. A major methodological challenge is to find a suitable parametrization for the GEV distribution when covariates or latent spatial effects are involved. Other challenges involve balancing model complexity and parsimony using an appropriate model selection procedure, and making inference using a reliable and computationally efficient approach. Our approach relies on a latent Gaussian modeling framework with a novel multivariate link function designed to separate the interpretation of the parameters at the latent level and to avoid unreasonable estimates of the shape and time trend parameters. Structured additive regression models are proposed for the four parameters at the latent level. For computational efficiency with large datasets and richly parametrized models, we exploit an accurate and fast approximate Bayesian inference approach. We applied our proposed methodology to annual peak river flow data from 554 catchments across the United Kingdom (UK). Our model performed well in terms of flood predictions for both gauged and ungauged catchments. The results show that the spatial model components for the transformed location and scale parameters, and the time trend, are all important. Posterior estimates of the time trend parameters correspond to an average increase of about $1.5\%$ per decade and reveal a spatial structure across the UK. To estimate return levels for spatial aggregates, we further develop a novel copula-based post-processing approach of posterior predictive samples, in order to mitigate the effect of the conditional independence assumption at the data level, and we show that our approach provides accurate results.

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arXiv2021

Tractable Bayes of Skew-Elliptical Link Models for Correlated Binary Data

Correlated binary response data with covariates are ubiquitous in longitudinal or spatial studies. Among the existing statistical models the most well-known one for this type of data is the multivariate probit model, which uses a Gaussian link to model dependence at the latent level. However, a symmetric link may not be appropriate if the data are highly imbalanced. Here, we propose a multivariate skew-elliptical link model for correlated binary responses, which includes the multivariate probit model as a special case. Furthermore, we perform Bayesian inference for this new model and prove that the regression coefficients have a closed-form unified skew-elliptical posterior. The new methodology is illustrated by application to COVID-19 pandemic data from three different counties of the state of California, USA. By jointly modeling extreme spikes in weekly new cases, our results show that the spatial dependence cannot be neglected. Furthermore, the results also show that the skewed latent structure of our proposed model improves the flexibility of the multivariate probit model and provides better fit to our highly imbalanced dataset.

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arXiv2021

Conex-Connect: Learning Patterns in Extremal Brain Connectivity From Multi-Channel EEG Data

Epilepsy is a chronic neurological disorder affecting more than 50 million people globally. An epileptic seizure acts like a temporary shock to the neuronal system, disrupting normal electrical activity in the brain. Epilepsy is frequently diagnosed with electroencephalograms (EEGs). Current methods study the time-varying spectra and coherence but do not directly model changes in extreme behavior. Thus, we propose a new approach to characterize brain connectivity based on the joint tail behavior of the EEGs. Our proposed method, the conditional extremal dependence for brain connectivity (Conex-Connect), is a pioneering approach that links the association between extreme values of higher oscillations at a reference channel with the other brain network channels. Using the Conex-Connect method, we discover changes in the extremal dependence driven by the activity at the foci of the epileptic seizure. Our model-based approach reveals that, pre-seizure, the dependence is notably stable for all channels when conditioning on extreme values of the focal seizure area. Post-seizure, by contrast, the dependence between channels is weaker, and dependence patterns are more "chaotic". Moreover, in terms of spectral decomposition, we find that high values of the high-frequency Gamma-band are the most relevant features to explain the conditional extremal dependence of brain connectivity.

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arXiv2020

Estimating high-resolution Red Sea surface temperature hotspots, using a low-rank semiparametric spatial model

In this work, we estimate extreme sea surface temperature (SST) hotspots, i.e., high threshold exceedance regions, for the Red Sea, a vital region of high biodiversity. We analyze high-resolution satellite-derived SST data comprising daily measurements at 16703 grid cells across the Red Sea over the period 1985-2015. We propose a semiparametric Bayesian spatial mixed-effects linear model with a flexible mean structure to capture spatially-varying trend and seasonality, while the residual spatial variability is modeled through a Dirichlet process mixture (DPM) of low-rank spatial Student-$t$ processes (LTPs). By specifying cluster-specific parameters for each LTP mixture component, the bulk of the SST residuals influence tail inference and hotspot estimation only moderately. Our proposed model has a nonstationary mean, covariance and tail dependence, and posterior inference can be drawn efficiently through Gibbs sampling. In our application, we show that the proposed method outperforms some natural parametric and semiparametric alternatives. Moreover, we show how hotspots can be identified and we estimate extreme SST hotspots for the whole Red Sea, projected until the year 2100, based on the Representative Concentration Pathways 4.5 and 8.5. The estimated 95\% credible region for joint high threshold exceedances include large areas covering major endangered coral reefs in the southern Red Sea.

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