Genomic Prediction Using Bayesian Regression Models With Global–Local Prior

Bayesian regression models are widely used in genomic prediction for various species. By introducing the global parameter τ which can shrink marker effects to zero, and the local parameter λ_k which can allow markers with large effects to escape from the shrinkage, we developed two novel Bayesian models, named BayesHP and BayesHE. The BayesHP model uses Horseshoe+ prior, while the BayesHE model assumes local parameter λ_k follow a half-t distribution with unknown degree of freedom. The performances of BayesHP and BayesHE models were compared to three classical prediction models including GBLUP, BayesA, and BayesB, and BayesU which also applied global-local prior (Horseshoe prior). To assess model performances for traits with various genetic architectures simulated data and real data in cattle (milk production, health, and type traits) and mice (type, and growth traits) were analyzed. The results of simulation data analysis indicated that models based on global-local priors, including BayesU, BayesHP and BayesHE, performed better in traits with higher heritability and fewer QTL. The results of real data analysis showed that BayesHE was optimal or suboptimal for all traits, whereas BayesHP was superior to other classical models only for milk production traits. For BayesHE, its flexibility to estimate hyperparameter automatically allows the model to be more adaptable to a wider range of traits. The BayesHP model, however, tended to be suitable for traits having major/large QTL, given its nature of the “U” type-like shrinkage pattern. Our results suggested that auto-estimate the degree of freedom (e.g., BayesHE) would be a better choice other than increase the layers of local parameter (e.g., BayesHP). In this study, we introduced the global-local prior with unknown hyperparameter to Bayesian regression models for genomic prediction, which can trigger further investigations on model development.