Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học thế giới đề tài: A comparison of strategies for Markov chain Monte Carlo computation in quantitative genetics | Genet. Sel. Evol. 40 2008 161-176 INRA EDP Sciences 2008 DOI gse 2007042 Available online at Original article A comparison of strategies for Markov chain Monte Carlo computation in quantitative genetics Rasmus WAAGEPETERSEN1 Noelia IbAnEZ-ESCRICHE2 Daniel Sorensen3 1 Department of Mathematical Sciences Aalborg University 9220 Aalborg Denmark 2IRTA Avda. Rovira Roure 25198 Lleida Spain 3 Department of Genetics and Biotechnology Danish Institute of Agricultural Sciences . Box 50 8830 Tjele Denmark Received 14 February 2007 accepted 7 September 2007 Abstract - In quantitative genetics Markov chain Monte Carlo MCMC methods are indispensable for statistical inference in non-standard models like generalized linear models with genetic random effects or models with genetically structured variance heterogeneity. A particular challenge for MCMC applications in quantitative genetics is to obtain efficient updates of the high-dimensional vectors of genetic random effects and the associated covariance parameters. We discuss various strategies to approach this problem including reparameterization Langevin-Hastings updates and updates based on normal approximations. The methods are compared in applications to Bayesian inference for three data sets using a model with genetically structured variance heterogeneity Langevin-Hastings Markov chain Monte Carlo normal approximation proposal distributions reparameterization 1. INTRODUCTION Given observations of a trait and a pedigree for a group of animals the basic model in quantitative genetics is a linear mixed model with genetic random effects. The correlation matrix of the genetic random effects is determined by the pedigree and is typically very high-dimensional but with a sparse inverse. Maximum likelihood inference and Bayesian inference for the linear mixed model are well-studied topics 16 . Regarding Bayesian inference with appropriate choice of priors the full conditional distributions are .
