Classification basée sur des mélanges de modèles hiérarchiques bivariés

International audienceLes approches probabilistes basées sur les modèles de mélange sont de plus en plus utilisées en classification automatique car elles fournissent un cadre formel pour résoudre des problèmes pratiques qui se posent en classification, tels que la détermination du nombre de classes, et permettent d'estimer l'incertitude associée à la classification. Les limites de ces méthodes résident principalement dans le choix de la loi de probabilité des composantes du mélange, qui dépend du type de données et va contraindre la forme des classes. Peu de modèles de mélange ont été étudiés dans le cas multivarié, et il est difficile d'adapter la méthode d'estimation d'une distribution à une autre. Nous proposons une généralisation des méthodes de classification basées sur des modèles de mélange qui : - s'adapte rapidement à des données de type différents (continues, discrètes, binaires, surdispersées), - permet d'obtenir des formes de classe et des structures de corrélation variées, - permet de traiter des données multivariées comportant des observations de plusieurs types. Pour cela nous considérons un modèle hiérarchique, dans lequel la couche cachée est issue d'un mélange de lois gaussiennes bivariées et la couche d'observation est obtenue par une distribution bivariée dont le choix dépend du type de données observées. L'estimation du modèle se fait par un algorithme MCEM

Modelling the Evolutionary Dynamics of Viruses within Their Hosts: A Case Study Using High-Throughput Sequencing

Uncovering how natural selection and genetic drift shape the evolutionary dynamics of virus populations within their hosts can pave the way to a better understanding of virus emergence. Mathematical models already play a leading role in these studies and are intended to predict future emergences. Here, using high-throughput sequencing, we analyzed the within-host population dynamics of four Potato virus Y (PVY) variants differing at most by two substitutions involved in pathogenicity properties. Model selection procedures were used to compare experimental results to six hypotheses regarding competitiveness and intensity of genetic drift experienced by viruses during host plant colonization. Results indicated that the frequencies of variants were well described using Lotka-Volterra models where the competition coefficients βij exerted by variant j on variant i are equal to their fitness ratio, rj/ri. Statistical inference allowed the estimation of the effect of each mutation on fitness, revealing slight (s = −0.45%) and high (s = −13.2%) fitness costs and a negative epistasis between them. Results also indicated that only 1 to 4 infectious units initiated the population of one apical leaf. The between-host variances of the variant frequencies were described using Dirichlet-multinomial distributions whose scale parameters, closely related to the fixation index FST, were shown to vary with time. The genetic differentiation of virus populations among plants increased from 0 to 10 days post-inoculation and then decreased until 35 days. Overall, this study showed that mathematical models can accurately describe both selection and genetic drift processes shaping the evolutionary dynamics of viruses within their hosts

Should I Stay or Should I Go? A Habitat-Dependent Dispersal Kernel Improves Prediction of Movement

The analysis of animal movement within different landscapes may increase our understanding of how landscape features affect the perceptual range of animals. Perceptual range is linked to movement probability of an animal via a dispersal kernel, the latter being generally considered as spatially invariant but could be spatially affected. We hypothesize that spatial plasticity of an animal's dispersal kernel could greatly modify its distribution in time and space. After radio tracking the movements of walking insects (Cosmopolites sordidus) in banana plantations, we considered the movements of individuals as states of a Markov chain whose transition probabilities depended on the habitat characteristics of current and target locations. Combining a likelihood procedure and pattern-oriented modelling, we tested the hypothesis that dispersal kernel depended on habitat features. Our results were consistent with the concept that animal dispersal kernel depends on habitat features. Recognizing the plasticity of animal movement probabilities will provide insight into landscape-level ecological processes

Uniform iterated logarithm laws for martingales and their application to functional estimation in controlled Markov chains

International audienc

Semigroup stationary processes and spectral representation

International audienc

Quelques propriétés des surfaces rationnelles du second degré

* INRA, Centre d'Avignon, Documentation, Domaine St Paul, Site Agroparc, 84914 Avignon cedex 9 Diffusion du document : INRA, Centre d'Avignon, Documentation, Domaine St Paul, Site Agroparc, 84914 Avignon cedex 9National audienc

Reducing Non-Stationary Stochastic Processes to Stationarity By a Time Deformation

A necessary and sufficient condition is given to reduce a non-stationary random process fZ(t) : t 2 T ` Rg to stationarity via a bijective differentiable time deformation \Phi so that its correlation function r(t; t 0 ) depends only on the difference \Phi(t 0 )\Gamma\Phi(t) through a stationary correlation function R: r(t; t 0 ) = R(\Phi(t 0 ) \Gamma \Phi(t))