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Multivariate Bayesian analysis of Gaussian, right censored Gaussian, ordered categorical and binary traits using Gibbs sampling

  • Inge Riis KorsgaardEmail author
  • Mogens Sandø Lund
  • Daniel Sorensen
  • Daniel Gianola
  • Per Madsen
  • Just Jensen
Open Access
Research

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.

Keywords

categorical Gaussian multivariate Bayesian analysis right censored Gaussian 

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Copyright information

© INRA, EDP Sciences 2003

This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.

Authors and Affiliations

  • Inge Riis Korsgaard
    • 1
    Email author
  • Mogens Sandø Lund
    • 1
  • Daniel Sorensen
    • 1
  • Daniel Gianola
    • 2
  • Per Madsen
    • 1
  • Just Jensen
    • 1
  1. 1.Department of Animal Breeding and GeneticsDanish Institute of Agricultural SciencesTjeleDenmark
  2. 2.Department of Meat and Animal SciencesUniversity of Wisconsin-MadisonUSA

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