arXiv subjects

Jean-François Coeurjolly

Publications and source records attributed to Jean-François Coeurjolly.

At least 19 recordsLinked to original sources

arXiv2026

Marked point processes intensity estimation using sparse group Lasso method applied to locations of lucrative and cooperative banks in mainland France

In this paper, we model the locations of five major banks in mainland France, two lucrative and three cooperative institutions based on socio-economic considerations. Locations of banks are collected using web scrapping and constitute a bivariate spatial point process for which we estimate nonparametrically summary functions (intensity, Ripley and cross-Ripley's K functions). This shows that the pattern is highly inhomogenenous and exhibits a clustering effect especially at small scales, and thus a significant departure to the bivariate (inhomogeneous) Poisson point process is pointed out. We also collect socio-economic datasets (at the living area level) from INSEE and propose a parametric modelling of the intensity function using these covariates. We propose a group-penalized bivariate composite likelihood method to estimate the model parameters, and we establish its asymptotic properties. The application of the methodology to the banking dataset provides new insights into the specificity of the cooperative model within the sector, particularly in relation to the theories of institutional isomorphism.

stat.ME↗

arXiv2026

Existence, properties, and parametric inference for possibly hyperuniform Gibbs perturbed lattices

This work lies at the intersection of Gibbs models and hyperuniform point processes. Classical Gibbs models, whether defined on lattices or in continuous space, provide flexible tools to describe interacting particle systems but are generally not hyperuniform. Conversely, known hyperuniform models such as the Ginibre process or perturbed lattices lack flexibility and typically cannot enforce physically relevant constraints such as hard-core interactions. We introduce a new class of models, termed Gibbs perturbed lattice models, which preserve a lattice structure while allowing interactions through a Hamiltonian defined on the perturbed particle locations. We establish existence results for the associated Gibbs measures, derive DLR-type equilibrium equations, and show that some models in this class exhibit hyperuniformity. Finally, we propose statistical inference methods based on the Takacs-Fiksel type approach and prove their asymptotic properties.

math.PR↗

arXiv2026

When Imbalance Comes Twice: Active Learning under Simulated Class Imbalance and Label Shift in Binary Semantic Segmentation

The aim of Active Learning is to select the most informative samples from an unlabelled set of data. This is useful in cases where the amount of data is large and labelling is expensive, such as in machine vision or medical imaging. Two particularities of machine vision are first, that most of the images produced are free of defects, and second, that the amount of images produced is so big that we cannot store all acquired images. This results, on the one hand, in a strong class imbalance in defect distribution and, on the other hand, in a potential label shift caused by limited storage. To understand how these two forms of imbalance affect active learning algorithms, we propose a simulation study based on two open-source datasets. We artificially create datasets for which we control the levels of class imbalance and label shift. Three standard active learning selection strategies are compared: random sampling, entropy-based selection, and core-set selection. We demonstrate that active learning strategies, and in particular the entropy-based and core-set selections, remain interesting and efficient even for highly imbalanced datasets. We also illustrate and measure the loss of efficiency that occurs in the situation a strong label shift.

cs.CV↗

arXiv2026

Simulation of warping processes with applications to temperature data

Curve registration plays a major role in functional data analysis by separating amplitude and phase variation through warping functions and the accurate simulation of warping processes is essential for developing statistical methods that properly account for phase variability in functional data. In this paper, we focus on the simulation of continuous warping processes with a prescribed expectation and a controllable variance. We study and compare three procedures, including two existing methods and a new algorithm based on randomized empirical cumulative distribution functions. For each approach, we provide an operational description and establish theoretical results for the first two moments of the simulated processes. A numerical study illustrates the theoretical findings and highlights the respective merits of the three methods. Finally, we present an application to the analysis of temperature distributions in Montreal based on simulated realizations from a warping process estimated from temperature quantile functions.

stat.ME↗

arXiv2025

Semi-parametric Markov models for multi-type point patterns

Multi-type Markov point processes offer a flexible framework for modelling complex multi-type point patterns where it is pertinent to capture both interactions between points as well as large scale trends depending on observed covariates. However, estimation of interaction and covariate effects may be seriously biased in the presence of unobserved spatial confounders. In this paper we introduce a new class of semi-parametric Markov point processes that adjusts for spatial confounding through a non-parametric factor that accommodates effects of latent spatial variables common to all types of points. We introduce a conditional pseudo likelihood for parameter estimation and show that the resulting estimator has desirable asymptotic properties. Our methodology not least has great potential in studies of industry agglomeration and we apply it to study spatial patterns of locations of two types of banks in France.

stat.ME↗

arXiv2025

Critical Point Processes Obtained from a Gaussian Random Field with a View Towards Statistics

This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical points of latent smooth Gaussian random fields or of subsets of critical points like minima, saddle points etc. Despite of the simplicity of their definition, the mathematical analysis of critical point processes is non-trivial involving for example deep results on the geometry of random fields, Sobolev space theory, chaos expansions, and multiple Wiener-It{ô} integrals. We provide explicit expressions for fundamental moment characteristics used in spatial point process statistics like the intensity parameter, the pair correlation function, and higher order intensity functions. The crucial dependence structure (attraction or repulsiveness) of a critical point process is discussed in depth and is in particular related to the dimension of the points and the type of critical points (extrema, saddle points, or all of the critical points). We propose simulation strategies based on spectral methods or smoothing of grid-based simulations and show that resulting approximate critical point process simulations asymptotically converge to the exact critical point process distribution. Finally, under the increasing domain framework, we obtain asymptotic results for linear and bilinear statistics of a critical point process. In particular, we obtain a multivariate central limit theorem for the intensity parameter estimate and a modified version of Ripley's K-function.

math.PR↗

arXiv2024

Spatio-temporal point process intensity estimation using zero-deflated subsampling applied to a lightning strikes dataset in France

Cloud-to-ground lightning strikes observed in a specific geographical domain over time can be naturally modeled by a spatio-temporal point process. Our focus lies in the parametric estimation of its intensity function, incorporating both spatial factors (such as altitude) and spatio-temporal covariates (such as field temperature, precipitation, etc.). The events are observed in France over a span of three years. Spatio-temporal covariates are observed with resolution $0.1^\circ \times 0.1^\circ$ ($\approx 100$km$^2$) and six-hour periods. This results in an extensive dataset, further characterized by a significant excess of zeroes (i.e., spatio-temporal cells with no observed events). We reexamine composite likelihood methods commonly employed for spatial point processes, especially in situations where covariates are piecewise constant. Additionally, we extend these methods to account for zero-deflated subsampling, a strategy involving dependent subsampling, with a focus on selecting more cells in regions where events are observed. A simulation study is conducted to illustrate these novel methodologies, followed by their application to the dataset of lightning strikes.

stat.ME↗

arXiv2024

Exploring first and second-order spatio-temporal structures of lightning strike impacts in the French Alps using subsampling

We model cloud-to-ground lightning strike impacts in the French Alps over the period 2011-2021 (approximately 1.4 million of events) using spatio-temporal point processes. We investigate first and higher-order structure for this point pattern and address the questions of homogeneity of the intensity function, first-order separability and dependence between events. The tuning of nonparametric methods and the different tests we consider in this study make the computational cost very expensive. We therefore suggest different subsampling strategies to achieve these tasks.

math.ST↗

arXiv2023

Regularization techniques for inhomogeneous (spatial) point processes intensity and conditional intensity estimation

Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on inhomogeneous parametric forms of these functions assumed to depend on a certain number of spatial covariates. When this number of covariates is large, we are faced with a high-dimensional problem. This paper provides an overview of these questions and existing solutions based on regularizations.

math.ST↗

arXiv2023

Pairwise interaction function estimation of Gibbs point processes using basis expansion

The class of Gibbs point processes (GPP) is a large class of spatial point processes able to model both clustered and repulsive point patterns. They are specified by their conditional intensity, which for a point pattern $\mathbf{x}$ and a location $u$, is roughly speaking the probability that an event occurs in an infinitesimal ball around $u$ given the rest of the configuration is $\mathbf{x}$. The most simple and natural class of models is the class of pairwise interaction point processes where the conditional intensity depends on the number of points and pairwise distances between them. This paper is concerned with the problem of estimating the pairwise interaction function non parametrically. We propose to estimate it using an orthogonal series expansion of its logarithm. Such an approach has numerous advantages compared to existing ones. The estimation procedure is simple, fast and completely data-driven. We provide asymptotic properties such as consistency and asymptotic normality and show the efficiency of the procedure through simulation experiments and illustrate it with several datasets.

math.ST↗

arXiv2022

Adaptive lasso and Dantzig selector for spatial point processes intensity estimation

Lasso and Dantzig selector are standard procedures able to perform variable selection and estimation simultaneously. This paper is concerned with extending these procedures to spatial point process intensity estimation. We propose adaptive versions of these procedures, develop efficient computational methodologies and derive asymptotic results for a large class of spatial point processes under an original setting where the number of parameters, i.e. the number of spatial covariates considered, increases with the expected number of data points. Both procedures are compared theoretically, in a simulation study, and in a real data example.

stat.ME↗

arXiv2021

Monte Carlo integration of non-differentiable functions on $[0,1]^ι$, $ι=1,\dots,d$, using a single determinantal point pattern defined on $[0,1]^d$

This paper concerns the use of a particular class of determinantal point processes (DPP), a class of repulsive spatial point processes, for Monte Carlo integration. Let $d\ge 1$, $I\subseteq \overline d=\{1,\dots,d\}$ with $ι=|I|$. Using a single set of $N$ quadrature points $\{u_1,\dots,u_N\}$ defined, once for all, in dimension $d$ from the realization of the DPP model, we investigate "minimal" assumptions on the integrand in order to obtain unbiased Monte Carlo estimates of $μ(f_I)=\int_{[0,1]^ι} f_I(u) \mathrm{d} u$ for any known $ι$-dimensional integrable function on $[0,1]^ι$. In particular, we show that the resulting estimator has variance with order $N^{-1-(2s\wedge 1)/d}$ when the integrand belongs to some Sobolev space with regularity $s > 0$. When $s>1/2$ (which includes a large class of non-differentiable functions), the variance is asymptotically explicit and the estimator is shown to satisfy a Central Limit Theorem.

stat.CO↗

arXiv2021

A convolution type model for the intensity of spatial point processes applied to eye-movement data

Estimating the first-order intensity function in point pattern analysis is an important problem, and it has been approached so far from different perspectives: parametrically, semiparametrically or nonparametrically. Our approach is close to a semiparametric one. Motivated by eye-movement data, we introduce a convolution type model where the log-intensity is modelled as the convolution of a function $β(\cdot)$, to be estimated, and a single spatial covariate (the image an individual is looking at for eye-movement data). Based on a Fourier series expansion, we show that the proposed model \rev{can be viewed as a} log-linear model with an infinite number of coefficients, which correspond to the spectral decomposition of $β(\cdot)$. After truncation, we estimate these coefficients through a penalized Poisson likelihood. We illustrate the efficiency of the proposed methodology on simulated data and on eye-movement data.

stat.ME↗

arXiv2021

Inference for possibly high-dimensional inhomogeneous Gibbs point processes

Gibbs point processes (GPPs) constitute a large and flexible class of spatial point processes with explicit dependence between the points. They can model attractive as well as repulsive point patterns. Feature selection procedures are an important topic in high-dimensional statistical modeling. In this paper, composite likelihood approach regularized with convex and non-convex penalty functions is proposed to handle statistical inference for possibly high-dimensional inhomogeneous GPPs. The composite likelihood incorporates both the pseudo-likelihood and the logistic composite likelihood. We particularly investigate the setting where the number of covariates diverges as the domain of observation increases. Under some conditions provided on the spatial GPP and on the penalty functions, we show that the oracle property, the consistency and the asymptotic normality hold. Our results also cover the low-dimensional case which fills a large gap in the literature. Through simulation experiments, we validate our theoretical results and finally, an application to a tropical forestry dataset illustrates the use of the proposed approach.

math.ST↗

arXiv2020

Digit analysis for Covid-19 reported data

The coronavirus which appeared in December 2019 in Wuhan has spread out worldwide and caused the death of more than 280,000 people (as of May, 11 2020). Since February 2020, doubts were raised about the numbers of confirmed cases and deaths reported by the Chinese government. In this paper, we examine data available from China at the city and provincial levels and we compare them with Canadian provincial data, US state data and French regional data. We consider cumulative and daily numbers of confirmed cases and deaths and examine these numbers through the lens of their first two digits and in particular we measure departures of these first two digits to the Newcomb-Benford distribution, often used to detect frauds. Our finding is that there is no evidence that cumulative and daily numbers of confirmed cases and deaths for all these countries have different first or second digit distributions. We also show that the Newcomb-Benford distribution cannot be rejected for these data.

stat.AP↗

arXiv2020

Information criteria for inhomogeneous spatial point processes

The theoretical foundation for a number of model selection criteria is established in the context of inhomogeneous point processes and under various asymptotic settings: infill, increasing domain, and combinations of these. For inhomogeneous Poisson processes we consider Akaike information criterion and the Bayesian information criterion, and in particular we identify the point process analogue of sample size needed for the Bayesian information criterion. Considering general inhomogeneous point processes we derive new composite likelihood and composite Bayesian information criteria for selecting a regression model for the intensity function. The proposed model selection criteria are evaluated using simulations of Poisson processes and cluster point processes.

math.ST↗

arXiv2020

Projections of determinantal point processes

Let $\mathbf x=\{x^{(1)},\dots,x^{(n)}\}$ be a space filling-design of $n$ points defined in $[0{,}1]^d$. In computer experiments, an important property seeked for $\mathbf x$ is a nice coverage of $[0{,}1]^d$. This property could be desirable as well as for any projection of $\mathbf x$ onto $[0{,}1]^ι$ for $ι<d$ . Thus we expect that $\mathbf x_I=\{x_I^{(1)},\dots,x_I^{(n)}\}$, which represents the design $\mathbf x$ with coordinates associated to any index set $I\subseteq\{1,\dots,d\}$, remains regular in $[0{,}1]^ι$ where $ι$ is the cardinality of $I$. This paper examines the conservation of nice coverage by projection using spatial point processes, and more specifically using the class of determinantal point processes. We provide necessary conditions on the kernel defining these processes, ensuring that the projected point process $\mathbf{X}_I$ is repulsive, in the sense that its pair correlation function is uniformly bounded by 1, for all $I\subseteq\{1,\dots,d\}$. We present a few examples, compare them using a new normalized version of Ripley's function. Finally, we illustrate the interest of this research for Monte-Carlo integration.

math.PR↗

arXiv2019

Regularized estimation for highly multivariate log Gaussian Cox processes

Statistical inference for highly multivariate point pattern data is challenging due to complex models with large numbers of parameters. In this paper, we develop numerically stable and efficient parameter estimation and model selection algorithms for a class of multivariate log Gaussian Cox processes. The methodology is applied to a highly multivariate point pattern data set from tropical rain forest ecology.

stat.ME↗