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Edith Gabriel

Publications and source records attributed to Edith Gabriel.

12 recordsLinked to original sources
arXiv2026

Transformer-based Diffusion models for Hydrological Time Series Probabilistic Imputation and Forecasting

The modeling of hydrometeorological time series with limited observations is a key challenge in the monitoring of hydro-systems and water resources, as well as for flood or drought risk assessment. Due to the high variability of the underlying processes and the sparsity of available measurements, traditional statistical approaches often struggle to accurately represent their dynamics. In this context, recent advances in deep learning offer a promising direction for improving the representation and generation of complex temporal processes sampled at several observation sites. This study investigates the application of transformer-based diffusion models to the simulation and reconstruction of hydrological time series. The proposed framework is applied to the joint modeling of water quantity and quality at six sites spread across three adjacent headwater catchments located in North-East France on a limestone plateau covered by forests and field crops. The model is calibrated and validated using available observational data, which has been quality controlled and corrected for sensor drift and malfunction through collaborative efforts by LNE metrology expertise and Andra monthly quality control over more than 15 years. Its performance is compared with several established baseline approaches commonly used for time series modeling. Quantitative evaluation metrics are employed to assess the ability of the proposed method to reproduce key temporal characteristics of the observed signals in two settings: the imputation of incomplete time series and the forecasting of upcoming hydrological conditions. Results support the effectiveness of the transformer-based approach and highlight its capacity to capture and simulate the complex patterns present in hydrological data. In particular, the results indicate that diffusion models can efficiently sample realistic time series distributions under observation settings with variable missing data for both forecasting and imputation.

stat.ML↗
arXiv2023

A spatio-temporal hybrid Strauss hardcore point process for forest fire occurrences

We propose a new point process model that combines, in the spatio-temporal setting, both multi-scaling by hybridization and hardcore distances. Our so-called hybrid Strauss hardcore point process model allows different types of interaction, at different spatial and/or temporal scales, that might be of interest in environmental and biological applications. The inference and simulation of the model are implemented using the logistic likelihood approach and the birth-death Metropolis-Hastings algorithm. Our model is illustrated and compared to others on two datasets of forest fire occurrences respectively in France and Spain.

stat.AP↗
arXiv2021

Mapping the intensity function of a non-stationary point process in unobserved areas

Seismic networks provide data that are used as basis both for public safety decisions and for scientific research. Their configuration affects the data completeness, which in turn, critically affects several seismological scientific targets (e.g., earthquake prediction, seismic hazard...). In this context, a key aspect is how to map earthquakes density in seismogenic areas from censored data or even in areas that are not covered by the network. We propose to predict the spatial distribution of earthquakes from the knowledge of presence locations and geological relationships, taking into account any interaction between records. Namely, in a more general setting, we aim to estimate the intensity function of a point process, conditional to its censored realization, as in geostatistics for continuous processes. We define a predictor as the best linear unbiased combination of the observed point pattern. We show that the weight function associated to the predictor is the solution of a Fredholm equation of second kind. Both the kernel and the source term of the Fredholm equation are related to the first-and second-order characteristics of the point process through the intensity and the pair correlation function. Results are presented and illustrated on simulated non-stationary point processes and real data for mapping Greek Hellenic seismicity in a region with unreliable and incomplete records.

stat.ME↗
arXiv2020

On spatial and spatio-temporal multi-structure point process models

Spatial and spatio-temporal single-structure point process models are widely used in epidemiology, biology, ecology, seismology... . However, most natural phenomena present multiple interaction structure or exhibit dependence at multiple scales in space and/or time, leading to define new spatial and spatio-temporal multi-structure point process models. In this paper, we investigate and review such multi-structure point process models mainly based on Gibbs and Cox processes.

stat.ME↗
arXiv2020

Landscape allocation: stochastic generators and statistical inference

In agricultural landscapes, the composition and spatial configuration of cultivated and semi-natural elements strongly impact species dynamics, their interactions and habitat connectivity. To allow for landscape structural analysis and scenario generation, we here develop statistical tools for real landscapes composed of geometric elements including 2D patches but also 1D linear elements such as hedges. We design generative stochastic models that combine a multiplex network representation and Gibbs energy terms to characterize the distributional behavior of landscape descriptors for land-use categories. We implement Metropolis-Hastings for this new class of models to sample agricultural scenarios featuring parameter-controlled spatial and temporal patterns (e.g., geometry, connectivity, crop-rotation). Pseudolikelihood-based inference allows studying the relevance of model components in real landscapes through statistical and functional validation, the latter achieved by comparing commonly used landscape metrics between observed and simulated landscapes. Models fitted to subregions of the Lower Durance Valley (France) indicate strong deviation from random allocation, and they realistically capture small-scale landscape patterns. In summary, our approach of statistical modeling improves the understanding of structural and functional aspects of agro-ecosystems, and it enables simulation-based theoretical analysis of how landscape patterns shape biological and ecological processes.

q-bio.PE↗
arXiv2020

Point-process based Bayesian modeling of space-time structures of forest fire occurrences in Mediterranean France

Due to climate change and human activity, wildfires are expected to become more frequent and extreme worldwide, causing economic and ecological disasters. The deployment of preventive measures and operational forecasts can be aided by stochastic modeling that helps to understand and quantify the mechanisms governing the occurrence intensity. We here develop a point process framework for wildfire ignition points observed in the French Mediterranean basin since 1995, and we fit a spatio-temporal log-Gaussian Cox process with monthly temporal resolution in a Bayesian framework using the integrated nested Laplace approximation (INLA). Human activity is the main direct cause of wildfires and is indirectly measured through a number of appropriately defined proxies related to land-use covariates (urbanization, road network) in our approach, and we further integrate covariates of climatic and environmental conditions to explain wildfire occurrences. We include spatial random effects with Mat\'ern covariance and temporal autoregression at yearly resolution. Two major methodological challenges are tackled: first, handling and unifying multi-scale structures in data is achieved through computer-intensive preprocessing steps with GIS software and kriging techniques; second, INLA-based estimation with high-dimensional response vectors and latent models is facilitated through intra-year subsampling, taking into account the occurrence structure of wildfires.

stat.AP↗
arXiv2019

A spatio-temporal multi-scale model for Geyer saturation point process: application to forest fire occurrences

Because most natural phenomena exhibit dependence at multiple scales like locations of earthquakes or forest fire occurrences, spatio-temporal single-scale point process models are unrealistic in many applications. This motivates us to construct generalizations of classical Gibbs models. In this paper, we extend the Geyer saturation point process model to the spatio-temporal multi-scale framework. The simulation process is carried out through a birth-death Metropolis-Hastings algorithm. In a simulation study, we compare two common methods for statistical inference in Gibbs models: the pseudo-likelihood and logistic likelihood approaches that we tailor to this model. Finally, we illustrate this new model on forest fire occurrences modeling in Southern France.

stat.AP↗
arXiv2016

Predicting the intensity of partially observed data from a revisited kriging for point processes

We consider a stationary and isotropic spatial point process whose a realisation is observed within a large window. We assume it to be driven by a stationary random field $U$. In order to predict the local intensity of the point process, $\lambda (x|U)$, we propose to define the first- and second-order characteristics of a random field, defined as the regularized counting process, from the ones of the point process and to interpolate the local intensity by using a kriging adapted to the regularized process.

stat.ME↗
arXiv2014

Weighted M-estimators for multivariate clustered data: theory and simulation results

We study weighted M-estimators for $\mathbb{R}^d$-valued clustered data and give sufficient conditions for their consistency. Their asymptotic normality is established with estimation of the asymptotic covariance matrix. We address the robustness of these estimators in terms of their breakdown point. Comparison with the unweighted case is performed with some numerical studies. They highlight that optimal weights maximizing the relative efficiency have a bad impact on the breakdown point.

math.ST↗
arXiv2014

Predicting the intensity of partially observed data from a revisited kriging for point processes

We consider a stationary and isotropic spatial point process, whose a realisation is observed within a large window. In order to predict its local intensity, we propose to define the first- and second-order characteristics of a random field, defined as the regularized counting process, from the ones of the point process and to interpolate the intensity by using a revisited kriging of the regularized process.

stat.ME↗
arXiv2013

Estimating second-order characteristics of inhomogeneous spatio-temporal point processes: influence of edge correction methods and intensity estimates

We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In particular, the space-time inhomogeneous pair correlation function and $K$-function measure the spatio-temporal clustering/regularity and the spatio-temporal interaction, and thus help with model choice. Non-parametric estimators of the second-order characteristics require information from outside the study region, resulting to the so-called edge effects which have to be corrected, and depend on first-order characteristics, which have to be estimated in practice. Here, we extend classical edge correction factors to the spatio-temporal setting and compare the performance of the related estimators for stationary/non-stationary and/or isotropic/anisotropic point patterns. Then, we explore the influence of estimated intensity function on these estimators.

math.ST↗