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Therefore, the residuals associated with genes in a replicate, standardized by the estimated gene wise variances, should show a normal distribution.
Compared with simply averaging replicate spots, this method greatly improves the precision with which the gene wise variances are estimated.
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where μ L and μ R are the mean values of the feature over all trials for classes L and R, respectively, and (σ L )2 and (σ R )2 are the trial-wise variances of the feature.
An empirical Bayes smoothing of gene-wise variances was conducted according to Smyth et al. [57].
Various parameter constellations for the true treatment means and the stage-wise variances are considered.
The moderated variances replace the probe-wise variances in the t- and F-statistic calculations.
One such procedure is limma (Smyth, 2004), where an empirical Bayes model is used to moderate the probe-wise variances.
We have proposed a novel approach called Tshrink+ for inferring differential gene expression through improved modelling of the gene-wise variances.
Existing methods share information between genes of similar average expression by shrinking, or moderating, the gene-wise variances to a fitted common variance.
This is to avoid over-parameterization and help the variance estimation when some studies in meta-analysis lack enough samples to produce stable estimates of the gene-wise variances.
In the second scenario, a random selection of 50% of the animals from the training dataset was used in the Bayesian models and RR-BLUP, and the BLUP-C and BLUP-SSVS used the SNP-wise variances from BayesC and BSSVS, with the corresponding reduced data.
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