Genomic Prediction Using Bayesian Regression Models With Global-Local Prior

Abstract

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, whereas the BayesHE model assumes local parameter λ _k , after a half-t distribution with an unknown degree of freedom. The performances of BayesHP and BayesHE models were compared with 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 quantitative trait locus. The results of real data analysis showed that BayesHE was optimal or suboptimal for all traits, whereas BayesHP was not superior to other classical models. 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 quantitative trait locus, 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 increasing the local parameter layers (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.

Keywords: Horseshoe; Horseshoe+ prior; half-Cauchy; half-t distribution; hyperparameter estimating.