title: Variational bayesian method of estimating variance components.
abstract: We developed a Bayesian analysis approach by using a variational inference method, a so-called variational Bayesian method, to determine the posterior distributions of variance components. This variational Bayesian method and an alternative Bayesian method using Gibbs sampling were compared in estimating genetic and residual variance components from both simulated data and publically available real pig data. In the simulated data set, we observed strong bias toward overestimation of genetic variance for the variational Bayesian method in the case of low heritability and low population size, and less bias was detected with larger population sizes in both methods examined. The differences in the estimates of variance components between the variational Bayesian and the Gibbs sampling were not found in the real pig data. However, the posterior distributions of the variance components obtained with the variational Bayesian method had shorter tails than those obtained with the Gibbs sampling. Consequently, the posterior standard deviations of the genetic and residual variances of the variational Bayesian method were lower than those of the method using Gibbs sampling. The computing time required was much shorter with the variational Bayesian method than with the method using Gibbs sampling.
authors.affiliation: Animal Genome Research Unit, National Institute of Agrobiological Sciences, Tsukuba, Ibaraki, Japan.
authors.forename: Aisaku
authors.initials: A
authors.lastname: Arakawa
authors.affiliation: Animal Genome Research Unit, National Institute of Agrobiological Sciences, Tsukuba, Ibaraki, Japan.
authors.forename: Masaaki
authors.initials: M
authors.lastname: Taniguchi
authors.affiliation: Agroinformatics Division, National Agriculture and Food Research Organization, Agricultural Research Center, Tsukuba, Ibaraki, Japan.
authors.forename: Takeshi
authors.initials: T
authors.lastname: Hayashi
authors.affiliation: Animal Genome Research Unit, National Institute of Agrobiological Sciences, Tsukuba, Ibaraki, Japan.
authors.forename: Satoshi
authors.initials: S
authors.lastname: Mikawa
mesh_terms: D000818:Animals; D001499:Bayes Theorem; D001947:Breeding; D066264:Datasets as Topic; D014644:Genetic Variation; D055106:Genome-Wide Association Study; D016014:Linear Models; D008390:Markov Chains; D009010:Monte Carlo Method; D013552:Swine / Q000235:genetics*
keywords: Gibbs sampling; linear mixed model; spectral decomposition