tailieunhanh - Báo cáo khoa hoc:" Alternative implementations of Monte Carlo EM algorithms for likelihood inferences"

Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học thế giới đề tài: Alternative implementations of Monte Carlo EM algorithms for likelihood inferences | Genet Sei. Evol. 33 2001 443-452 INRA EDP Sciences 2001 443 Note Alternative implementations of Monte Carlo EM algorithms for likelihood inferences Louis Alberto García-Cortésa Daniel Sorensenb a Departamento de Genética Universidad de Zaragoza Calle Miguel Servet 177 Zaragoza 50013 Spain b Section of Biometrical Genetics Department of Animal Breeding and Genetics Danish Institute of Agricultural Sciences PB 50 8830 Tjele Denmark Received 14 September 2000 accepted 23 April 2001 Abstract - Two methods of computing Monte Carlo estimators of variance components using restricted maximum likelihood via the expectation-maximisation algorithm are reviewed. A third approach is suggested and the performance of the methods is compared using simulated data. restricted maximum likelihood Markov chain Monte Carlo EM algorithm Monte Carlo variance variance components 1. introduction The expectation-maximisation EM algorithm 1 to obtain restricted maximum likelihood REML estimators of variance components 7 is widely used. The expectation part of the algorithm can be demanding in highly dimensional problems because it requires the inverse of a matrix of the order of the number of location parameters of the model. In animal breeding this can be of the order of hundred of thousands or millions. Guo and Thompson 3 proposed a Markov chain Monte Carlo MCMC approximation to the computation of these expectations. This is useful because in principle it allows to analyse larger data sets but at the expense of introducing Monte Carlo noise. Thompson 9 suggested a modihcation to the algorithm which reduces this noise. The purpose of this note is to review briefly these two approaches and to suggest a third one which can be computationally competitive to the Thompson estimator. Correspondence and reprints E-mail sorensen@ 444 . García-Cortés D. Sorensen 2. the model and the em-reml equations The sampling model for the data is assumed to be y b s sf N Xb C ZS Isf where y is the