Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Bayesian analysis of mixed linear models via Gibbs sampling with an application to litter size in Iberian pigs CS Wang | 91 Genet Sei Evol 1994 26 91-115 Elsevier INRA Original article Bayesian analysis of mixed linear models via Gibbs sampling with an application to litter size in Iberian pigs cs Wang J J Rutledge D Gianola University of Wisconsin-Madison Department of Meat and Animal Science Madison WI 53706-1284 USA Received 26 April 1993 accepted 17 December 1993 Summary - The Gibbs sampling is a Monte-Carlo procedure for generating random samples from joint distributions through sampling from and updating conditional distributions. Inferences about unknown parameters are made by 1 computing directly summary statistics from the samples or 2 estimating the marginal density of an unknown and then obtaining summary statistics from the density. All conditional distributions needed to implement the Gibbs sampling in a univariate Gaussian mixed linear model are presented in scalar algebra so no matrix inversion is needed in the computations. For location parameters all conditional distributions are univariate normal whereas those for variance components are scaled inverted chi-squares. The procedure was applied to solve a Gaussian animal model for litter size in the Gamito strain of Iberian pigs. Data were 1 213 records from 426 dams. The model had farrowing season 72 levels and parity 4 as fixed effects breeding values 597 permanent environmental effects 426 and residuals were random. In CASE I variances were assumed known with REML restricted maximum likelihood estimates used as true parameter values. Here means and variances of the posterior distributions of all effects were obtained by inversion from the mixed model equations. These exact solutions were used to check the Monte-Carlo estimates given by Gibbs using 120 000 samples. Linear regression slopes of true posterior means on Gibbs means were almost exactly 1 for fixed additive genetic and permanent environmental effects. Regression slopes of true posterior variances on Gibbs variances were and respectively. In
