title: Bayesian genomic-enabled prediction as an inverse problem.
abstract: Genomic-enabled prediction in plant and animal breeding has become an active area of research. Many prediction models address the collinearity that arises when the number (p) of molecular markers (e.g. single-nucleotide polymorphisms) is larger than the sample size (n). Here we propose four Bayesian approaches to the problem based on commonly used data reduction methods. Specifically, we use a Gaussian linear model for an orthogonal transformation of both the observed data and the matrix of molecular markers. Because shrinkage of estimates is affected by the prior variance of transformed effects, we propose four structures of the prior variance as a way of potentially increasing the prediction accuracy of the models fitted. To evaluate our methods, maize and wheat data previously used with standard Bayesian regression models were employed for measuring prediction accuracy using the proposed models. Results indicate that, for the maize and wheat data sets, our Bayesian models yielded, on average, a prediction accuracy that is 3% greater than that of standard Bayesian regression models, with less computational effort.
authors.affiliation: Colegio de Posgraduados, 56230, Montecillo, Texcoco, Edo. de México.
authors.forename: Jaime
authors.initials: J
authors.lastname: Cuevas
authors.affiliation: Colegio de Posgraduados, 56230, Montecillo, Texcoco, Edo. de México.
authors.forename: Sergio
authors.initials: S
authors.lastname: Pérez-Elizalde
authors.affiliation: Universidad de Quintana Roo, Chetumal, Quintana Roo, México.
authors.forename: Victor
authors.initials: V
authors.lastname: Soberanis
authors.affiliation: Colegio de Posgraduados, 56230, Montecillo, Texcoco, Edo. de México.
authors.forename: Paulino
authors.initials: P
authors.lastname: Pérez-Rodríguez
authors.affiliation: Department of Animal Sciences, University of Wisconsin, Madison, Wisconsin 53706.
authors.forename: Daniel
authors.initials: D
authors.lastname: Gianola
authors.affiliation: Biometrics and Statistics Unit, International Maize and Wheat Improvement Center (CIMMYT), 06600, México, D.F., México j.crossa@cgiar.org.
authors.forename: José
authors.initials: J
authors.lastname: Crossa
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D016678:Genome; D018745:Genome, Plant; D008957:Models, Genetic; D012984:Software; D014908:Triticum / Q000235:genetics; D003313:Zea mays / Q000235:genetics
keywords: Bayesian regression; GenPred; genomic selection; inverse regression; prior distribution; shared data resources; shrinkage