Genet. Sel. Evol. 36 (2004) 49-64
DOI: 10.1051/gse:2003050

Full conjugate analysis of normal multiple traits with missing records using a generalized inverted Wishart distribution

Rodolfo Juan Carlos Cantet^{a, b}, Ana Nélida Birchmeier^a and Juan Pedro Steibel<sup>a

a</sup>  Departamento de Producción Animal, Universidad de Buenos Aires, Avenida San Martín 4453, 1417 Buenos Aires, Argentina
^b  Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina

(Received 15 January 2003; accepted 7 August 2003)

Abstract
A Markov chain Monte Carlo (MCMC) algorithm to sample an exchangeable covariance matrix, such as the one of the error terms ( ) 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 , 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.

Key words: FCG algorithm / multiple traits / missing data / conjugate priors / normal-inverted Wishart

Correspondence and reprints: rcantet@agro.uba.ar

© INRA, EDP Sciences 2004