Computation of all eigenvalues of matrices used in restricted maximum likelihood estimation of variance components using sparse matrix techniques

Restricted maximum likelihood (REML) estimates of variance components have desirable properties but can be very expensive computationally. Large costs result from the need for the repeated inversion of the large coefficient matrix of the mixed-model equations. This paper presents a method based on the computation of all eigenvalues using the Lanczos method, a technique reducing a large sparse symmetric matrix to a tridiagonal form. Dense matrix inversion is not required. It is accurate and not very demanding on storage requirements. The Lanczos method, the computation of eigenvalues, its application in a genetic context, and an example are presented.Les estimations du maximum de vraisemblance restreinte (REML) des composantes de variance ont des propriétés intéressantes mais peuvent être coûteuses en temps de calcul et en besoin de mémoire. Le problème vient de la nécessité d’inverser de façon répétée la matrice des coefficients des équations du modèle mixte. Cet article présente une méthode basée sur le calcul des valeurs propres et sur l’utilisation de la méthode de Lanczos, une technique permettant de réduire une matrice creuse, symétrique et de grande taille en une matrice tridiagonale. L’inversion de matrices denses n’est pas nécessaire. Cette méthode donne des résultats précis et ne demande que très peu de stockage en mémoire. La méthode de Lanczos, le calcul des valeurs propres, son application dans le contexte génétique et un exemple sont présentés

Genetic variation of traits measured in several environments. II. Inference on between-environment homogeneity of intra-class correlations

This paper describes a further contribution to the problem of testing homogeneity of intra-class correlations among environments in the case of univariate linear models, without making any assumption about the genetic correlation between environments. An iterative generalized expectation-maximization (EM) algorithm, as described in Foulley and Quaas (1994), is presented for computing restricted maximum likelihood (REML) estimates of the residual and between-family components of variance and covariance. Three different parameterizations (cartesian, polar and spherical coordinates) are proposed to compute EM-REML estimators under the reduced (constant intra-class correlation between environments) model. This procedure is illustrated with the analysis of simulated data.Cet article décrit une approche permettant d’estimer les composantes de variance-covariance entre milieux dans le cas de corrélation intra-classe homogènes entre milieux, sans faire d’hypothèse sur les corrélations génétiques entre milieux pris 2 à 2. Un algorithme itératif d’espérance-maximisation (EM), comparable à celui décrit par Foulley et Quaas (1994), est proposé pour calculer les estimations du maximum de vraisemblance restreinte (REML) des composantes résiduelles et familiales de variance covariance. Trois paramétrisations différentes (coordonnées cartésiennes, polaires et sphériques) sont proposées pour calculer les estimateurs EM-REML sous le modèle réduit (les corrélations intra-classe sont supposées toutes égales à une même constante). Cette procédure est illustrée par l’analyse de données simulées

The cases of June 2000, November 2002 and September 2002 as examples of Mediterranean floods

International audienceFour flood events that affected three different countries are here described in terms of meteorological genesis and in terms of consequences on the population and on the territory. Each event is a good representative of a class of phenomena that produce important effects on the urban and extra-urban tissue and that must be taken into account in an optic of civil protection and risk evaluation. This is the subject of the HYDROPTIMET project, part of the Interreg IIIB program, which is collocated in the framework of the prevention of natural hazards and, in particular, those related to severe meteo-hydrological events. This paper aims at being a general introduction of the four events which are the subject of more detailed studies, already published or under submission

Concurrent Geometric Multicasting

We present MCFR, a multicasting concurrent face routing algorithm that uses geometric routing to deliver a message from source to multiple targets. We describe the algorithm's operation, prove it correct, estimate its performance bounds and evaluate its performance using simulation. Our estimate shows that MCFR is the first geometric multicast routing algorithm whose message delivery latency is independent of network size and only proportional to the distance between the source and the targets. Our simulation indicates that MCFR has significantly better reliability than existing algorithms

Estimation of genetic parameters of egg production traits of laying hens by restricted maximum likelihood applied to a multiple-trait reduced animal model

International audienc

TORRENTIAL RAIN EVENTS OVER THE CÉVENNES-VIVARAIS REGION

High resolution numerical simulations of recent flash-flood events that have occurred over Mediterranean coasts are used to underline the physical mechanisms leading to the stationary of the precipitating systems and the predictability associated with such events. Three cases, including the two last extreme flash-flood events over Southeastern France, have been simulated : the 12-13 November 1999 catastrophe over the Aude region (MAP IOP16), the 8-9 September 2002 flash-flood over the Gard region and the less paroxysmal event of 13-14 October 1995 over the Cévennes-Vivarais relief. Sensitivity to the initial conditions, to the Massif Central relief and to the Sea Surface Temperature (SST) has been studied