Analyse statistique des processus ponctuels spatio-temporels de propagation sur une grille
Institution:
Antilles-GuyaneDisciplines:
Directors:
Abstract EN:
The origin of the work presented in this thesis is a problem of epidemiology in the field of agricultural crops. It is to model the spread of disease on an experimental plot. Individuals statistics, in this case the plants of this plot, are regularly arranged on the nodes on a grid. In such situations, harvest data, in general, dates successive positions of the new infected individuals, putting in place various strategies depending on the size of parcels or human resources and technology available. Ifone is not limited by the cost and effort of observation, the ideal method is to make the exhaustive sampling ie observe the condition ofeach individual on the plot. However, for reasons ofcost observation, we can not have the status of individuals on the grid than the dates of observation data. There fore, if at date S t_OS we have all infected plants S 1_{t_O}S and at date S t_lS we have S1_{t_l}S, a methodological approach is to consider the possible order of infection between S t_0S and S t_l S. The purpose ofthis work is to propose a model for the spatial and temporal evolution of a disease on a regular grid and develop statistical inference of this model for data consisting of infection cards reported on dates fixed widely spaced so that the precise dates ofinfection are missing data. The plan of this thesis in to two parts. \\ In the first, we recall the main tools ofstatistical analysis of ad hoc spatial and/or temporal processes, and a summary on Bayesi an analysis and Markovian exploration techniques which will be used to infer and optimize the parameters of interest. In the second part of the thesis, we present a model inspired by the propagation model Gibson (1996) and various methodologies to tackle the problem of statistical inference in Chapter 3. The proposed methods can be classified in to two broad families. As a first step, we can consider inference techniques that take into account only the temporal order ofarrival of events between the dates ofobservation St_0S and St_lS. These techniques range from the use of simple Monte Carlo methods to generation of Markov chain. In a second time, the methodology is to generate the precise dates of occurrence of events between the dates of observations S t_0S and S t_l St, then usin the theory of Bayes combined with Markov chains to estimate the parameters of interest.
Abstract FR:
L'origine du travail présenté dans cette thèse est un problème d'épidémiologie dans le domaine des cultures agricoles. Il s'agit de modéliser la propagation d'une maladie sur une parcelle expérimentale. Les individus statistiques, en l'occurence les plantes de cette parcelle, sont disposés de façon régulière sur les noeuds d'une grille. Dans ce type de situation, on récolte les données , en général, à des dates successives, les positions des nouveaux individus infectés, en mettant e place diverses stratégies suivant la taille des parcelles ou encore des moyens humains et technologiques disponibles. Si l'on est pas limité par le coût et l'effort d'observation, la m"thode idéale consiste à faire de l'échantillonnage exhaustif, c'est-à-dire observer l'état de chaque individu sur la parcelle. Cependant, pour des raisons de coût d'observation, on ne peut avoir l'état des individus sur la grille qu'à des dates d'observations données. Par conséquent, si si à S t_0S on possède l'ensemble des plntes infectées S I 8 {t _0}S et à S t_ 1S on possède S I_ {t_I}, une approche méthodologique est de considérer l'ordre possible d'infection des plantes entre S t_0S et S t_IS