Member of the Statistics Team, Laboratory of Mathematics (LMA), Avignon University.
Long term visitor (since September 2014) at Biostatistics and spatial processes Unit, INRA-Avignon.
Spatial and spatio-temporal point processes
Predicting the conditional intensity of a spatial point process
- Collaborations with: Joël Chadoeuf and Pascal Monestiez (Biostatistic and spatial processes unit of the French National Institute for Agricultural Research), Florent Bonneu (Laboratory of Mathematics, Avignon University).
- Aim: Predicting a spatial point process is a challenging issue. Our aim is thus to answer the following issues:
(i) Observing the full pattern within a large window W, how to estimate the conditional intensity? And is there an optimal grid size for the interpolation? (ii) Having a partially observed pattern within W, how to predict the conditional intensity?
- Methods: In order to achieve this, we assume that the process is stationary and isotropic, and that it is obtained by a weak dependent process with a parameter driven by a stationary random field at a larger scale. In order to predict the local intensity, we propose to define the first- and second-order characteristics of the random field (i.e mean and variogram) from the ones of the point process (i.e. intensity and pair correlation function) and to interpolate the conditional intensity by using a revisited ordinary kriging, whose weights depend on the local structure of the point process. Hence, our method uses all the data to locally predict at a given point, which it is not the case of kernel methods, and it also uses the information at fine scale of the point process, which it is not the case in geostatistical approaches. Furthermore, it does not require a specific model but only (an estimation of) the first- and second-order characteristics of the point process.
Spatio-temporal point processes in human epidemiology
- Collaborations with: Division of medicine and department of Mathematics and Statistics (Lancaster University ), Liverpool Veterinary School and Manchester Royal Infirmary.
- Aim: The project is on investigating the origins, transmission pathways and emergence of human Campylobacter infections.
In collaboration with Pr Peter Diggle et le Dr Daniel Wilson, I have developed statistical methods for describing spatio-temporal and genetic epidemiology of human infectious diseases.
- Methods: Our method is based on second-order characteristics of spatio-temporal point processes. They are used to test for spatio-temporal clustering/inhibition and interaction. the Ripley K-function is extended to the inhomogeneous and spatio-temporal setting. We defined non-parametric estimators for the inhomogeneous and spatio-temporal pair correlation function and K-function.
Simulation of spatio-temporal point patterns
- Collaborations with: Peter J. Diggle and Barry Rowlingson (Lancaster University)
- Aim: We developed an R package for the simulation and analysis of spatio-temporal point patterns. This package, called stpp, is downloadable from here
Estimating second-order characteristics of inhomogeneous spatio-temporal point processes
Non-parametric estimates of the K-function and the pair correlation function play a fundamental role for exploratory and explanatory analysis of spatial and spatio-temporal point patterns. These estimates usually require information from outside of the study region, resulting to the so-called edge effects which have to be corrected. They also depend on first-order characteristics, which have to be estimated in practice. I extended classical edge correction methods to the spatio-temporal setting and compared the performance of the related estimators for stationary/non-stationary and/or isotropic/anisotropic point patterns. Further, I explored the influence of the estimated intensity function on these estimators.
Infestation strategy of spruce bark beetles
- Collaborations with: Etienne Toffin (Biological Control and Spatial Ecology Lab).
- Aim: We want to understand individual and collective behavior of the bark beetle.
We have shown that the main feature of attacks is a spacing mechanism, ie some competition between bark beetles, leading to some inhibition distance; and that distance varies, decreases, with respect to time and attacks' density. We are now interesting in modelling the attacks.
- Methods: Our analyses are based on second-order characteristics of point processes and on nearest neighbor distances.
Project on Robust and Optimal Locations for
Sustainable Environment and Systems
The aim of this interdisciplinary project is to provide to decision makers and planners of the geographic space reliable and relevant information allowing them to evaluate characteristics and properties of several centres in theoretical or practical geographic context, thus according to different spatial patterns of demand points.
Weighted M-estimators for clustered data
- Mohammed El Asri PhD thesis co-supervised with Delphine Blanke (Laboratory of Mathematics, Avignon University)
- Method : We study weighted M-estimators for R^d-valued clustered data. We give sufficient conditions for their convergence as well as their asymptotic normality. Robustness of these estimators is addressed via the study of their breakdown point. Numerical studies compare them with their unweighted version and highlight that optimal weights maximizing the relative efficiency lead to a degradation of their breakdown point..
New adaptive and robust estimators of location
- Collaborations with: Delphine Blanke (Laboratory of Mathematics, Avignon University), Didier Josselin (UMR ESPACE of Avignon University).
- Method : We developed new adaptive estimators, derived from 1818 Laplace's work, defined as a linear combination of the empirical mean and median. We compare them to classical location estimators as regards their robustness through a Monte Carlo study. Their behaviour is examined for different sample sizes and sampling distributions (centrally symmetric and asymmetric contaminated normals).
Modelling effect of herbicide on weeds and crop yield
- Collaborations with:S. Gaba (INRA, Dijon), V. Bretagnolle (CNRS, Chizé), J. Chadoeuf (INRA, Avignon) and F. Bonneu (LMA, UAPV)
- Aim: to model farmer behavior using an hidden state variable in the relationship between herbicide use, weed community and yield.
Hydromagnetic coupling in low noise environment
- Collaborations with: UMR EMMAH (Avignon University), the Low Noise Underground Laboratory of Rustrel and the Avignon Laboratory of Informatics
- Aim: The project aims at analysing the influence of hydrodynamic fluctuations on magnetic properties of the karstic aquifer under study, independently of seismic activities. I am analysing hydrogeological and magnetic data to define their inter-correlations.
Detecting zones of abrupt changes in spatial data
- PhD thesis: Obtained in December 2004, Montpellier University, France
Location: Unit of Biostatistics and Spatial Processes
PhD supervisor: Denis Allard
- Method :
Data : a spatial variable Z(x).
Method : (i) interpolation of the variable (by ordinary kriging) on the study domain, (ii) local test for detecting the existence of discontinuities in the mean of Z(.), (iii) global test of significance of the detected Zones of Abrupt Change.
Marie-Jeanne Laurent-Duhamel 2006 prize of the French statistical society (SFdS: Société Francaise de Statistique).