Controlling the Overfitting of Heritability in Genomic Selection through Cross Validation.

In genomic selection (GS), all the markers across the entire genome are used to conduct marker-assisted selection such that each quantitative trait locus of complex trait is in linkage disequilibrium with at least one marker. Although GS improves estimated breeding values and genetic gain, in most GS models genetic variance is estimated from training samples with many trait-irrelevant markers, which leads to severe overfitting in the calculation of trait heritability. In this study, we demonstrated overfitting heritability due to the inclusion of trait-irrelevant markers using a series of simulations, and such overfitting can be effectively controlled by cross validation experiment. In the proposed method, the genetic variance is simply the variance of the genetic values predicted through cross validation, the residual variance is the variance of the differences between the observed phenotypic values and the predicted genetic values, and these two resultant variance components are used for calculating the unbiased heritability. We also demonstrated that the heritability calculated through cross validation is equivalent to trait predictability, which objectively reflects the applicability of the GS models. The proposed method can be implemented with the Mixed Procedure in SAS or with our R package "GSMX" which is publically available at https://cran.r-project.org/web/packages/GSMX/index.html

Bayesian Mixture Model Analysis for Detecting Differentially Expressed Genes

Control-treatment design is widely used in microarray gene expression experiments. The purpose of such a design is to detect genes that express differentially between the control and the treatment. Many statistical procedures have been developed to detect differentially expressed genes, but all have pros and cons and room is still open for improvement. In this study, we propose a Bayesian mixture model approach to classifying genes into one of three clusters, corresponding to clusters of downregulated, neutral, and upregulated genes, respectively. The Bayesian method is implemented via the Markov chain Monte Carlo (MCMC) algorithm. The cluster means of down- and upregulated genes are sampled from truncated normal distributions whereas the cluster mean of the neutral genes is set to zero. Using simulated data as well as data from a real microarray experiment, we demonstrate that the new method outperforms all methods commonly used in differential expression analysis