A robust Bayesian genome-based median regression model

  • Abelardo Montesinos-López
  • Osval A. Montesinos-LópezEmail author
  • Enrique R. Villa-Diharce
  • Daniel GianolaEmail author
  • José Crossa
Original Article


Key message

Current genome-enabled prediction models assumed errors normally distributed, which are sensitive to outliers. We propose a model with errors assumed to follow a Laplace distribution to deal better with outliers.


Current genome-enabled prediction models use regressions that fit the expected value (mean) of a response variable with errors assumed normally distributed, which are often sensitive to outliers, either genetic or environmental. For this reason, we propose a robust Bayesian genome median regression (BGMR) model that fits regressions to the medians of a distribution, with errors assumed to follow a Laplace distribution to deal better with outliers. The BGMR model was evaluated under a Bayesian framework with Markov Chain Monte Carlo sampling using a location–scale mixture representation of the Laplace distribution. The BGMR was implemented with two simulated and two real genomic data sets, and we compared its prediction performance with that of a conventional genomic best linear unbiased prediction (GBLUP) model and the Laplace maximum a posteriori (LMAP) method. The prediction accuracies of BGMR were higher than those of the GBLUP and LMAP methods when there were outliers. The BGMR model could be useful to breeders who need to predict and select genotypes based on data with unknown outliers.



We thank all scientists, field workers, and lab assistants from National Programs and CIMMYT who collected the data used in this study. We acknowledge the financial support provided by the Foundation for Research Levy on Agricultural Products (FFL) and the Agricultural Agreement Research Fund (JA) in Norway through NFR Grant 267806. We are also thankful for the financial support provided by CIMMYT CRP (maize and wheat), the Bill & Melinda Gates Foundation, as well the USAID projects (Cornell University and Kansas State University) that financed the collection of the CIMMYT maize and wheat data analyzed in this study.

Compliance with ethical standards

Conflict of interest

The authors declare they do not have any conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI)Universidad de GuadalajaraGuadalajaraMexico
  2. 2.Facultad de TelemáticaUniversidad de ColimaColimaMexico
  3. 3.Departamento de EstadísticaCentro de Investigación en Matemáticas (CIMAT)GuanajuatoMexico
  4. 4.Departments of Animal Sciences, Dairy Science, and Biostatistics and Medical InformaticsUniversity of Wisconsin-MadisonMadisonUSA
  5. 5.Biometrics and Statistics Unit and Global Wheat ProgramInternational Maize and Wheat Improvement Center (CIMMYT)MexicoMexico

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