arXiv subjects

Jérémy Rohmer

Publications and source records attributed to Jérémy Rohmer.

8 recordsLinked to original sources

arXiv2026

Which modelling choices shape your interpolation map? An Optimal Transport sensitivity analysis for groundwater sulfate concentration

Spatial prediction maps are crucial for environmental management yet highly sensitive to subjective modelling choices such as, e.g., covariates, spatial dependence structures, or mesh resolution. We develop a workflow that attributes the resulting map uncertainty to these choices and is applicable to any spatial model, since it operates only on an ensemble of maps produced by propagating the choices through spatial prediction. This ensemble is then filtered to retain only models with acceptable predictive performance, reduced in dimension by principal component (PC) analysis, and the sensitivity of the resulting scores to each choice is quantified by global sensitivity analysis based on optimal transport (OT) metrics. We demonstrate the framework with Bayesian geostatistics applied to the spatial mapping of sulphate concentrations in groundwater of Paris Basin (France), which is key for assessing groundwater chemical quality and establishing the natural geochemical baseline of aquifers. For this application, the covariates, mesh resolution, covariance models, and priors are combined into 18000 candidate configurations. These are filtered by cross-validated root mean square error (RMSE) and 95% coverage of the prediction interval, and the retained configurations are then inferred on a high-resolution grid and reduced to its three PCs. The OT analysis identifies covariate selection (under 95% coverage) and mesh resolution (under RMSE) as the dominant sources of uncertainty to the PCs, and a negligible one for the choice of the covariance model.

stat.ME↗

arXiv2025

Augmented Quantization: Mixture Models for Risk-Oriented Sensitivity Analysis

A central question in risk analysis is to identify the factors that drive the system toward a specific hazardous outcome, such as the exceedance of a given threshold. When relying on numerical simulators, we propose to study the distribution of the inputs, transformed into uniform variables via their cumulative distributions, conditionally on the occurrence of the hazardous event. To represent this multivariate conditional distribution for sensitivity analysis, we introduce an original quantization approach based on estimating a mixture of Dirac and local uniform distributions. For each marginal of this mixture, a Dirac component indicates a strong influence of the corresponding variable, whereas a uniform component with wide support reflects weak influence. A notable advantage of this method is its ability to identify the regions of the input space that most strongly influence the occurrence of the risk event, while also capturing the joint effects of multiple variables. However, learning mixture models typically relies on likelihood-based methods, which are not well suited to mixtures involving singular or Dirac components. To address this, we propose an \emph{Augmented Quantization} method, a reformulation of the classical quantization problem based on the p-Wasserstein distance, which can be computed in very general distribution spaces. The performance of Augmented Quantization in estimating such mixture models is first demonstrated on analytical toy problems, and then applied to sensitivity analysis of both an analytical function and a practical flooding case study on a section of the Loire River.

stat.AP↗

arXiv2025

Simulation of extreme functionals in meteoceanic data: Application to surge evolution over tidal cycles

We investigate the influence of time-varying meteoceanic conditions on coastal flooding under the prism of rare events. Focusing on conditions observed over half tidal cycles, we observe that such data fall within the framework of functional extreme value theory, but violate standard assumptions due to temporal dependence and short-tailed behavior.a To address this, we propose a two-stage methodology. First, we introduce an autoregressive model to eliminate temporal dependence between cycles. Second, considering the model residuals, we adapt existing techniques based on Pareto processes. This allows us to build a simulator of extreme scenarios, by applying inverse transformations. These simulations depend on an initial time series, which can be randomly selected to tune the desired level of extremes. We validate the simulator performance by comparing simulated times series with observations, through several criteria, based on principal component analysis, extreme value analysis, and classification algorithms. The approach is applied to the surge data, on the G{â}vres site, located in southern Brittany, France.

stat.AP↗

arXiv2024

FunQuant: A R package to perform quantization in the context of rare events and time-consuming simulations

Quantization summarizes continuous distributions by calculating a discrete approximation. Among the widely adopted methods for data quantization is Lloyd's algorithm, which partitions the space into Voronoï cells, that can be seen as clusters, and constructs a discrete distribution based on their centroids and probabilistic masses. Lloyd's algorithm estimates the optimal centroids in a minimal expected distance sense, but this approach poses significant challenges in scenarios where data evaluation is costly, and relates to rare events. Then, the single cluster associated to no event takes the majority of the probability mass. In this context, a metamodel is required and adapted sampling methods are necessary to increase the precision of the computations on the rare clusters.

stat.CO↗

arXiv2024

Empirical quantification of rockfall reach probability: objective determination of appropriate topographic descriptor

For rockfall hazard assessment on areas more than several km2 in size, the quantification of runout probability is usually done empirically. Classical methods use statistical distributions of reach or energy angles derived from rockfall databases. However, other topographic descriptors can be derived from the topographic profiles along the rockfall path. Using a database of more than 4,000 profiles of rockfall paths, we determine which topographic descriptors are most appropriate for reach probability estimation, by comparing their statistical distributions for rockfall stopping points, and for points the rocks overtook. We show that the curvilinear length of the propagation path, and the area under the propagation path can improve propagation estimations, especially when they are computed only along the final portion of the propagation path. This is illustrated by comparing an experimental distribution of rockfall stopping points to the estimated distributions.

physics.geo-ph↗

arXiv2023

Quantizing rare random maps: application to flooding visualization

Visualization is an essential operation when assessing the risk of rare events such as coastal or river floodings. The goal is to display a few prototype events that best represent the probability law of the observed phenomenon, a task known as quantization. It becomes a challenge when data is expensive to generate and critical events are scarce, like extreme natural hazard. In the case of floodings, each event relies on an expensive-to-evaluate hydraulic simulator which takes as inputs offshore meteo-oceanic conditions and dyke breach parameters to compute the water level map. In this article, Lloyd's algorithm, which classically serves to quantize data, is adapted to the context of rare and costly-to-observe events. Low probability is treated through importance sampling, while Functional Principal Component Analysis combined with a Gaussian process deal with the costly hydraulic simulations. The calculated prototype maps represent the probability distribution of the flooding events in a minimal expected distance sense, and each is associated to a probability mass. The method is first validated using a 2D analytical model and then applied to a real coastal flooding scenario. The two sources of error, the metamodel and the importance sampling, are evaluated to quantify the precision of the method.

stat.AP↗

arXiv2019

Approximating Gaussian Process Emulators with Linear Inequality Constraints and Noisy Observations via MC and MCMC

Adding inequality constraints (e.g. boundedness, monotonicity, convexity) into Gaussian processes (GPs) can lead to more realistic stochastic emulators. Due to the truncated Gaussianity of the posterior, its distribution has to be approximated. In this work, we consider Monte Carlo (MC) and Markov Chain Monte Carlo (MCMC) methods. However, strictly interpolating the observations may entail expensive computations due to highly restrictive sample spaces. Furthermore, having (constrained) GP emulators when data are actually noisy is also of interest for real-world implementations. Hence, we introduce a noise term for the relaxation of the interpolation conditions, and we develop the corresponding approximation of GP emulators under linear inequality constraints. We show with various toy examples that the performance of MC and MCMC samplers improves when considering noisy observations. Finally, on 2D and 5D coastal flooding applications, we show that more flexible and realistic GP implementations can be obtained by considering noise effects and by enforcing the (linear) inequality constraints.

stat.ML↗

arXiv2018

Profile extrema for visualizing and quantifying uncertainties on excursion regions. Application to coastal flooding

We consider the problem of describing excursion sets of a real-valued function $f$, i.e. the set of inputs where $f$ is above a fixed threshold. Such regions are hard to visualize if the input space dimension, $d$, is higher than 2. For a given projection matrix from the input space to a lower dimensional (usually $1,2$) subspace, we introduce profile sup (inf) functions that associate to each point in the projection's image the sup (inf) of the function constrained over the pre-image of this point by the considered projection. Plots of profile extrema functions convey a simple, although intrinsically partial, visualization of the set. We consider expensive to evaluate functions where only a very limited number of evaluations, $n$, is available, e.g. $n<100d$, and we surrogate $f$ with a posterior quantity of a Gaussian process (GP) model. We first compute profile extrema functions for the posterior mean given $n$ evaluations of $f$. We quantify the uncertainty on such estimates by studying the distribution of GP profile extrema with posterior quasi-realizations obtained from an approximating process. We control such approximation with a bound inherited from the Borell-TIS inequality. The technique is applied to analytical functions ($d=2,3$) and to a $5$-dimensional coastal flooding test case for a site located on the Atlantic French coast. Here $f$ is a numerical model returning the area of flooded surface in the coastal region given some offshore conditions. Profile extrema functions allowed us to better understand which offshore conditions impact large flooding events.

stat.ME↗