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

  • 1, 2Email author,
  • 1 and
  • 1
Genetics Selection Evolution200436:49

https://doi.org/10.1186/1297-9686-36-1-49

  • Received: 15 January 2003
  • Accepted: 7 August 2003
  • Published:

Abstract

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.

Keywords

  • FCG algorithm
  • multiple traits
  • missing data
  • conjugate priors
  • normal-inverted Wishart

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Authors’ Affiliations

(1)
Departamento de Producción Animal, Universidad de Buenos Aires, Avenida San Martín 4453, 1417 Buenos Aires, Argentina
(2)
Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET), Argentina

Copyright

© INRA, EDP Sciences 2004

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