The relative effect of genomic information on efficiency of Bayesian analysis of the mixed linear model with unknown variance.

This work focuses on the effects of variable amount of genomic information in the Bayesian estimation of unknown variance components associated with single-step genomic prediction. We propose a quantitative criterion for the amount of genomic information included in the model and use it to study the relative effect of genomic data on efficiency of sampling from the posterior distribution of parameters of the single-step model when conducting a Bayesian analysis with estimating unknown variances. The rate of change of estimated variances was dependent on the amount of genomic information involved in the analysis, but did not depend on the Gibbs updating schemes applied for sampling realizations of the posterior distribution. Simulation revealed a gradual deterioration of convergence rates for the locations parameters when new genomic data were gradually added into the analysis. In contrast, the convergence of variance components showed continuous improvement under the same conditions. The sampling efficiency increased proportionally to the amount of genomic information. In addition, an optimal amount of genomic information in variance-covariance matrix that guaranty the most (computationally) efficient analysis was found to correspond a proportion of animals genotyped ***0.8. The proposed criterion yield a characterization of expected performance of the Gibbs sampler if the analysis is subject to adjustment of the amount of genomic data and can be used to guide researchers on how large a proportion of animals should be genotyped in order to attain an efficient analysis.