Marginal inferences about variance  components in a mixed linear model  using Gibbs sampling

Cs, Wang; Rutledge, J.J.; Gianola, D.

doi:10.1051/gse:19930103

Cited by 79 publications

(107 citation statements)

References 6 publications

Supporting

Mentioning

100

Contrasting

Unclassified

Order By: Relevance

“…Also, for reasons of clarity and focus, I omit the description of TIM (e.g. Wang et al, 1993;Sorensen, 1996) in this section, although I do consider combinations of the FPM and TIM in the analysis of simulated data.…”

Section: Methodsmentioning

confidence: 99%

On flexible finite polygenic models for multiple-trait evaluation

Bink

2002

Genet. Res.

View full text Add to dashboard Cite

SummaryFinite polygenic models (FPM) might be an alternative to the infinitesimal model (TIM) for the genetic evaluation of pedigreed multiple-generation populations for multiple quantitative traits. I present a general flexible Bayesian method that includes the number of genes in the FPM as an additional random variable. Markov-chain Monte Carlo techniques such as Gibbs sampling and the reversible jump sampler are used for implementation. Sampling of genotypes of all genes in the FPM is done via the use of segregation indicators. A broad range of FPM models, some combined with TIM, are empirically tested for the estimation of variance components and the number of genes in the FPM. Four simulation scenarios were studied, including genetic models with 5 or 50 additive independent diallelic genes affecting the traits, and random selection or selection on one of the traits was performed. The results in this study were based on ten replicates per simulation scenario. In the case of random selection, uniform priors on additive gene effects led to posterior mean estimates of genetic variance that were positively correlated with the number of genes fitted in the FPM. In the case of trait selection, assuming normal priors on gene effects also led to genetic variance estimates for the selected trait that were negatively correlated with the number of genes in the FPM. This negative correlation was not observed for the unselected trait. Treating the number of genes in the FPM as random revealed a positive correlation between prior and posterior mean estimates of this number, but the prior hardly affected the posterior estimates of genetic variance. Posterior inferences about the number of genes should be considered to be indicative where trait selection seems to improve the power of distinguishing between TIM and FPM. Based on the results of this study, I suggest not replacing TIM by the FPM, but combining TIM and FPM with the number of genes treated as random, to facilitate a highly flexible and thereby robust method for variance component estimation in pedigreed populations. Further study is required to explore the full potential of these models under different genetic model assumptions.

show abstract

Section: Methodsmentioning

confidence: 99%

On flexible finite polygenic models for multiple-trait evaluation

Bink

2002

Genet. Res.

View full text Add to dashboard Cite

show abstract

“…For threshold models and binary traits it has been shown that poor results can also be obtained when the posterior is close to an improper density [18]. Furthermore, impropriety of posteriors may not be easy to determine, implying the risk of obtaining misleading results [4,7,18,27].…”

Section: Introductionmentioning

confidence: 99%

Influence of priors in Bayesian estimation of genetic parameters for multivariate threshold models using Gibbs sampling

2007

View full text Add to dashboard Cite

-Simulated data were used to investigate the influence of the choice of priors on estimation of genetic parameters in multivariate threshold models using Gibbs sampling. We simulated additive values, residuals and fixed effects for one continuous trait and liabilities of four binary traits, and QTL effects for one of the liabilities. Within each of four replicates six different datasets were generated which resembled different practical scenarios in horses with respect to number and distribution of animals with trait records and availability of QTL information. (Co)Variance components were estimated using a Bayesian threshold animal model via Gibbs sampling. The Gibbs sampler was implemented with both a flat and a proper prior for the genetic covariance matrix. Convergence problems were encountered in > 50% of flat prior analyses, with indications of potential or near posterior impropriety between about round 10 000 and 100 000. Terminations due to non-positive definite genetic covariance matrix occurred in flat prior analyses of the smallest datasets. Use of a proper prior resulted in improved mixing and convergence of the Gibbs chain. In order to avoid (near) impropriety of posteriors and extremely poorly mixing Gibbs chains, a proper prior should be used for the genetic covariance matrix when implementing the Gibbs sampler.Gibbs sampling / multivariate threshold model / covariance estimates / flat prior / proper prior

show abstract

“…But there can be no actual distribution to which the Gibbs picture corresponds. This was the problem with the Gibbsbased conclusions of Wang et al (1993Wang et al ( , 1994 and as they used models for which a posterior distribution did not exist.…”

Section: IImentioning

confidence: 99%

“…The sole purpose of these initial iterations was to provide the chain with ample opportunity to misbehave and alert us that something may be wrong; it never did. We chose 15,000 because a typical burn-in would probably be in the hundreds (see Wang et al 1993) so that if our chain did not misbehave during the burn-in stage, neither would that of an unknowing experimenter.…”

Section: IImentioning

confidence: 99%