Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Restricted maximum likelihood estimation for animal models using derivatives of the likelihood | Genet Sei Evol 1996 28 23-49 Elsevier INRA 23 Original article Restricted maximum likelihood estimation for animal models using derivatives of the likelihood K Meyer SP Smith Animal Genetics and Breeding Unit University of New England Armidale NSW 2351 Australia Received 21 March 1995 accepted 9 October 1995 Summary - Restricted maximum likelihood estimation using first and second derivatives of the likelihood is described. It relies on the calculation of derivatives without the need for large matrix inversion using an automatic differentiation procedure. In essence this is an extension of the Cholesky factorisation of a matrix. A reparameterisation is used to transform the constrained optimisation problem imposed in estimating covariance components to an unconstrained problem thus making the use of Newton-Raphson and related algorithms feasible. A numerical example is given to illustrate calculations. Several modified Newton-Raphson and method of scoring algorithms are compared for applications to analyses of beef cattle data and contrasted to a derivative-free algorithm. restricted maximum likelihood derivative algorithm variance component estimation Resume Estimation du maximum de vraisemblance restreinte pour des modèles individuals par derivation de la vraisemblance. Cet article décrit une methode d estimation du maximum de vraisemblance restreinte utilisant les dérivées premiere et seconde de la vraisemblance. La méthode est basée sur une procedure de differenciation automatique ne nécessitant pas I inversion de grandes matrices. Elie constitue en fait une extension de la decomposition de Cholesky appliquée à une matrice. On utilise un paramétrage qui transforme le problème d optimisation avec contrainte que soulève I estimation des composantes de variance en un problème sans contrainte ce qui rend possible I utilisation d algorithmes de Newton-Raphson OU apparentés. Les calculs sont illustrés sur un exemple numérique. Plusieurs algorithmes de type .
