title: A Variational Bayes Genomic-Enabled Prediction Model with Genotype × Environment Interaction.
abstract: There are Bayesian and non-Bayesian genomic models that take into account G×E interactions. However, the computational cost of implementing Bayesian models is high, and becomes almost impossible when the number of genotypes, environments, and traits is very large, while, in non-Bayesian models, there are often important and unsolved convergence problems. The variational Bayes method is popular in machine learning, and, by approximating the probability distributions through optimization, it tends to be faster than Markov Chain Monte Carlo methods. For this reason, in this paper, we propose a new genomic variational Bayes version of the Bayesian genomic model with G×E using half-t priors on each standard deviation (SD) term to guarantee highly noninformative and posterior inferences that are not sensitive to the choice of hyper-parameters. We show the complete theoretical derivation of the full conditional and the variational posterior distributions, and their implementations. We used eight experimental genomic maize and wheat data sets to illustrate the new proposed variational Bayes approximation, and compared its predictions and implementation time with a standard Bayesian genomic model with G×E. Results indicated that prediction accuracies are slightly higher in the standard Bayesian model with G×E than in its variational counterpart, but, in terms of computation time, the variational Bayes genomic model with G×E is, in general, 10 times faster than the conventional Bayesian genomic model with G×E. For this reason, the proposed model may be a useful tool for researchers who need to predict and select genotypes in several environments.
authors.affiliation: Facultad de Telemática, Universidad de Colima, 28040, México.
authors.forename: Osval A
authors.initials: OA
authors.lastname: Montesinos-López
authors.affiliation: Departamento de Matemáticas, Centro Universitario de Ciencias Exactas e Ingenierías (CUCEI), Universidad de Guadalajara, 44430, Jalisco, México.
authors.forename: Abelardo
authors.initials: A
authors.lastname: Montesinos-López
authors.affiliation: Biometrics and Statistics Unit and Global Wheat Program of the 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
authors.affiliation: Departamento de Estadística, Centro de Investigación en Matemáticas (CIMAT), 36240 Guanajuato, México.
authors.forename: José Cricelio
authors.initials: JC
authors.lastname: Montesinos-López
authors.affiliation: Facultad de Telemática, Universidad de Colima, 28040, México.
authors.forename: Francisco Javier
authors.initials: FJ
authors.lastname: Luna-Vázquez
authors.affiliation: Colegio de Postgraduados, Campus Córdoba, Km. 348 Carretera Federal Córdoba-Veracruz, Amatlán de los Reyes, 94946, México.
authors.forename: Josafhat
authors.initials: J
authors.lastname: Salinas-Ruiz
authors.affiliation: Facultad de Telemática, Universidad de Colima, 28040, México.
authors.forename: José R
authors.initials: JR
authors.lastname: Herrera-Morales
authors.affiliation: Facultad de Telemática, Universidad de Colima, 28040, México.
authors.forename: Raymundo
authors.initials: R
authors.lastname: Buenrostro-Mariscal
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D005075:Biological Evolution; D059647:Gene-Environment Interaction; D023281:Genomics / Q000379:methods*; D005838:Genotype; D008957:Models, Genetic; D015233:Models, Statistical; D015203:Reproducibility of Results; D012641:Selection, Genetic; D014908:Triticum / Q000235:genetics; D003313:Zea mays / Q000235:genetics
keywords: GenPred; Genomic Selection; Shared Data Resources; genome-enabled prediction; multi-environment; variational Bayes