BayesR

BayesR is a Bayesian regression method used in genomic selection and association studies. It models the effects of single-nucleotide polymorphisms (SNPs) with a four-component Gaussian mixture prior, allowing some SNPs to have zero effect while others have small, moderate, or large effects.

For each SNP j, the effect β_j is drawn from a mixture with a point mass at zero and three nonzero normal components with distinct variances. The mixture proportions (pi_0, pi_1, pi_2, pi_3) and the component variances are treated as unknown parameters and are estimated from the data. The model includes a residual term e ~ N(0, σ_e^2 I). Inference is typically carried out with Markov chain Monte Carlo methods, such as Gibbs sampling, to sample SNP effects, component indicators, and variance parameters.

Inference outputs include posterior means or medians of SNP effects and posterior inclusion probabilities, which indicate the likelihood that a given SNP belongs to any of the nonzero components. These results can be used for genomic prediction or to identify genomic regions influencing traits.

BayesR is designed to accommodate a polygenic architecture where most SNPs have small effects but a subset have larger effects, while allowing a substantial fraction to have zero effects. It can offer improved predictive accuracy over earlier Bayesian methods in some traits and populations. Limitations include computational intensity for very large datasets and sensitivity to prior specifications for the mixture proportions and component variances.

The method is implemented in software such as GCTA and related genomic analysis tools and is applied in livestock and crop breeding, as well as human genetics, to improve genomic prediction and fine-mapping of complex traits.