La prime nette est un outil pratique de gestion des risques et l’une des mesures de risque les plus connues en assurance. Il est également connu sous le nom de principe de la valeur moyenne ($μ=E[X]$), le principe de prime le plus simple, équivalent à l’espérance de la variable de taille de sinistre (risque). Dans ce principe, le taux de prime est fixé égal à la valeur attendue du risque $X$ ($X ≥ 0$), de fonction de répartition $F$, qui est définie par \[\Pi=E[X]:=\int_0^\infty(1-F(x))\,dx\] où $Π:χ →\mathbb{R}$, appelée fonction de mesure du risque et $χ$ un ensemble de variables aléatoires réelles. En effet, il existe dans la littérature une grande variété d’estimateurs asymptotiquement normaux sur la base des données complètes.

Cependant, il arrive souvent en pratique que les données soient censurées pour une raison ou une autre de telle façon que les techniques d’estimation basées sur les données complètes deviennent inappropriées. On utilise dans ce travail la théorie des valeurs extrêmes pour proposer une estimation alternative pour les données censurées aléatoirement à droite. Sous des conditions modérées, nous établissons la normalité asymptotique de l’estimateur proposé. La preuve repose fortement sur l’approximation gaussienne de Brahmi et al. (2015), Stute (1995) et les résultats de Kaplan-Meier (1958).

^* En collaboration avec D. Meraghni et A. Necir.

Spatial confounding is a fundamental issue in spatial regression models which arises because spatial random eff ects, included to approximate unmeasured spatial variation, are typically not independent of covariates in the model. This can lead to signifi cant bias in covariate eff ect estimates. We develop a broad theoretical framework that brings mathematical clarity to the mechanisms of spatial confounding. Subsequently, we explore the potential of Bayesian methodology in alleviating spatial confounding and leveraging the understanding of how such confounding originates in the construction of prior distributions.

Cells make fate decisions in response to dynamic environments, and multicellular structures emerge from multiscale interplays among cells and genes in space and time. The recent single-cell genomics technology provides an unprecedented opportunity to profile cells for all their genes. While those measurements provide high-dimensional gene expression profiles for all cells, it requires fixing individual cells that lose many important spatiotemporal information. Is it possible to infer temporal relationships among cells from single or multiple snapshots? How to recover spatial interactions among cells, for example, cell-cell communication? In this talk I will present our newly developed computational tools to study cell fate in the context of single cells as a system. In particular, I will show dynamical models and machine-learning methods, with a focus on inference and analysis of transitional properties of cells and cell-cell communication using both high-dimensional single-cell and spatial transcriptomics, as well as multi-omics data for some cases. Through their applications to various complex systems in development, regeneration, and diseases, we show the discovery power of such methods in addition to identifying areas for further method development for spatiotemporal analysis of single-cell data.

Survival models with cure fractions, known as long-term survival models, are widely used in epidemiology to account for both immune and susceptible patients regarding a failure event. In such studies, it is also necessary to estimate unobservable heterogeneity caused by unmeasured prognostic factors. Moreover, the hazard function may exhibit a non-monotonic shape, specifically, an unimodal hazard function. In this article, we propose a long-term survival model based on a defective version of the Dagum distribution, incorporating a power variance function frailty term to account for unobservable heterogeneity. This model accommodates survival data with cure fractions and non-monotonic hazard functions. The distribution is reparameterized in terms of the cure fraction, with covariates linked via a logit link, allowing for direct interpretation of covariate effects on the cure fractionan uncommon feature in defective approaches. We present maximum likelihood estimation for model parameters, assess performance through Monte Carlo simulations, and illustrate the models applicability using two health-related datasets: severe COVID-19 in pregnant and postpartum women and patients with malignant skin neoplasms.

Mathematical modelling of infectious diseases involves a series of mathematical techniques and methods that make it possible to describe the dynamics of their transmission in populations. The incorporation of biological and epidemiological events related to these diseases into models, taking into account their intrinsic uncertainty, is essential to explain and predict their dynamics. This seminar introduces dynamic modelling and calibration techniques with uncertainty in two areas of epidemiology on real-world case studies: antibiotic resistance, specifically in the case study of colistin-resistant Acinetobacter baumannii, and vaccination strategies, in particular against influenza and human papillomavirus (HPV). Combining deterministic and stochastic mathematical modelling techniques, parameter analysis and calibration strategies, we can explain the observed epidemiological scenarios, predict their evolution and evaluate the efficacy of preventive public health interventions.