Cantet Rodolfo Juan Carlos, Birchmeier Ana Nélida, Steibel Juan Pedro
Departamento de Producción Animal, Universidad de Buenos Aires, Avenida San Martín 4453, 1417 Buenos Aires, Argentina.
Genet Sel Evol. 2004 Jan-Feb;36(1):49-64. doi: 10.1186/1297-9686-36-1-49.
A Markov chain Monte Carlo (MCMC) algorithm to sample an exchangeable covariance matrix, such as the one of the error terms (R0) in a multiple trait animal model with missing records under normal-inverted Wishart priors is presented. The algorithm (FCG) is based on a conjugate form of the inverted Wishart density that avoids sampling the missing error terms. Normal prior densities are assumed for the 'fixed' effects and breeding values, whereas the covariance matrices are assumed to follow inverted Wishart distributions. The inverted Wishart prior for the environmental covariance matrix is a product density of all patterns of missing data. The resulting MCMC scheme eliminates the correlation between the sampled missing residuals and the sampled R0, which in turn has the effect of decreasing the total amount of samples needed to reach convergence. The use of the FCG algorithm in a multiple trait data set with an extreme pattern of missing records produced a dramatic reduction in the size of the autocorrelations among samples for all lags from 1 to 50, and this increased the effective sample size from 2.5 to 7 times and reduced the number of samples needed to attain convergence, when compared with the 'data augmentation' algorithm.
提出了一种马尔可夫链蒙特卡罗（MCMC）算法，用于在正态-逆威沙特先验下对可交换协方差矩阵进行采样，例如具有缺失记录的多性状动物模型中误差项（R0）的协方差矩阵。该算法（FCG）基于逆威沙特密度的共轭形式，避免了对缺失误差项进行采样。假设对“固定”效应和育种值采用正态先验密度，而协方差矩阵假定遵循逆威沙特分布。环境协方差矩阵的逆威沙特先验是所有缺失数据模式的乘积密度。由此产生的MCMC方案消除了采样的缺失残差与采样的R0之间的相关性，这反过来又有减少达到收敛所需的样本总量的效果。在具有极端缺失记录模式的多性状数据集中使用FCG算法，使得从1到50的所有滞后的样本自相关大小显著降低，与“数据扩充”算法相比，这将有效样本大小提高了2.5至7倍，并减少了达到收敛所需的样本数量。
