Catherine Larédo

Pré-publication, Document de travail HAL Id : hal-01332630, version 1

Mixed effects models are popular tools for analyzing longitudinal data from several individuals simultaneously. Individuals are described by N independent stochastic processes (Xi(t), t ∈ [0, T ]), i = 1,. .. , N , defined by a stochastic differential equation with random effects. We assume that the drift term depends linearly on a random vector Φi and the diffusion coefficient depends on another linear random effect Ψi. For the random effects, we consider a joint parametric distribution leading to explicit approximate likelihood functions for discrete observations of the processes Xi on a fixed time interval. The asymptotic behaviour of the associated estimators is studied when both the number of individuals and the number of observations per individual tend to infinity. The estimation methods are investigated on simulated and real neuronal data.

Developing tools for visualizing DNA sequences is an important issue in the Barcoding context. Visualizing Barcode data can be put in a purely statistical context, unsupervised learning. Clustering methods combined with projection methods have two closely linked objectives, visualizing and finding structure in the data. Multidimensional scaling (MDS) and Self-organizing maps (SOM) are unsupervised statistical tools for data visualization. Both algorithms map data onto a lower dimensional manifold: MDS looks for a projection that best preserves pairwise distances while SOM preserves the topology of the data. Both algorithms were initially developed for Euclidean data and the conditions necessary to their good implementation were not satisfied for Barcode data. We developed a workflow consisting in four steps: collapse data into distinct sequences; compute a dissimilarity matrix; run a modified version of SOM for dissimilarity matrices to structure the data and reduce dimensionality; project the results using MDS. This methodology was applied to Astraptes fulgerator and Hylomyscus, an African rodent with debated taxonomy. We obtained very good results for both data sets. The results were robust against unbalanced species. All the species in Astraptes were well displayed in very distinct groups in the various visualizations, except for LOHAMP and FABOV that were mixed up. For Hylomyscus, our findings were consistent with known species, confirmed the existence of four unnamed taxa and suggested the existence of potentially new species.

Background: DNA barcoding aims to assign individuals to given species according to their sequence at a small locus, generally part of the CO1 mitochondrial gene. Amongst other issues, this raises the question of how to deal with within-species genetic variability and potential transpecific polymorphism. In this context, we examine several assignation methods belonging to two main categories: (i) phylogenetic methods (neighbour-joining and PhyML) that attempt to account for the genealogical framework of DNA evolution and (ii) supervised classification methods (k-nearest neighbour, CART, random forest and kernel methods). These methods range from basic to elaborate. We investigated the ability of each method to correctly classify query sequences drawn from samples of related species using both simulated and real data. Simulated data sets were generated using coalescent simulations in which we varied the genealogical history, mutation parameter, sample size and number of species. Results: No method was found to be the best in all cases. The simplest method of all, "one nearest neighbour", was found to be the most reliable with respect to changes in the parameters of the data sets. The parameter most influencing the performance of the various methods was molecular diversity of the data. Addition of genetically independent loci - nuclear genes - improved the predictive performance of most methods. Conclusion: The study implies that taxonomists can influence the quality of their analyses either by choosing a method best-adapted to the configuration of their sample, or, given a certain method, increasing the sample size or altering the amount of molecular diversity. This can be achieved either by sequencing more mtDNA or by sequencing additional nuclear genes. In the latter case, they may also have to modify their data analysis method.

ABSTRACT. This paper develops a new contrast process for parametric inference of general hidden Markov models, when the hidden chain has a non‐compact state space. This contrast is based on the conditional likelihood approach, often used for ARCH‐type models. We prove the strong consistency of the conditional likelihood estimators under appropriate conditions. The method is applied to the Kalman filter (for which this contrast and the exact likelihood lead to asymptotically equivalent estimators) and to the discretely observed stochastic volatility models.