Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học thế giới đề tài: Multivariate Bayesian analysis of Gaussian, right censored Gaussian, ordered categorical and binary traits using Gibbs sampling | 159 Genet Sei. Evol. 35 2003 159-183 INRA EDP Sciences 2003 DOI gse 2003002 Original article Multivariate BaYesian analysis of Gaussian right censored Gaussian ordered categorical and binary traits using Gibbs sampling Inge Riis Korsgaarda Mogens Sand0 Lunda Daniel Sorensena Daniel Gianolab Per Madsena Just Jensena a Department of Animal Breeding and Genetics Danish Institute of Agricultural Sciences PO Box 50 8830 Tjele Denmark b Department of Meat and Animal Sciences University of Wisconsin-Madison WI 53706-1284 USA Received 5 October 2001 accepted 3 September 2002 Abstract - a fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian right censored and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits with more than two categories or binary traits where the grouping is determined via thresholds on the underlying Gaussian scale the liability scale. Allowances are made for unequal models unknown covariance matrices and missing data. Having outlined the theory strategies for implementation are reviewed. These include joint sampling of location parameters efficient sampling from the fully conditional posterior distribution of augmented data a multivariate truncated normal distribution and sampling from the conditional inverse Wishart distribution the fully conditional posterior distribution of the residual covariance matrix. Finally a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed. categorical Gaussian multivariate Bayesian analysis right censored Gaussian 1. introduction In a series of problems it has been demonstrated that using the Gibbs sampler in conjunction with data augmentation makes it possible to obtain .
