arXiv subjects

Déborah Idier

Publications and source records attributed to Déborah Idier.

3 recordsLinked to original sources

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↗

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↗