Table 1. Prior densities available for regression coefficients in the BGLR package.

Model (prior density)	Hyperparameters	Treatment in BGLRa
Flat (FIXED)	Mean (μβ)	μβ = 0
	Variance $\left({\sigma }_{\beta }^2\right)$	${\sigma }_{\beta }^2=1\times 1^{10}$
Gaussian (BRR)	Mean (μβ)	μβ = 0
	Variance $\left({\sigma }_{\beta }^2\right)$	${\sigma }_{\beta }^2\sim {\chi }^{-2}$
Scaled-t (BayesA)	Degrees of freedom (dfβ)	User specified (default value, 5)
	Scale (Sβ)	Sβ ∼ Gamma
Double exponential (BL)	λ2	λ fixed, user specified, or λ2 ∼ Gamma, or $\lambda /\max \sim Beta$b
Gaussian mixture (BayesC)	π (prop. of nonnull effects)	π ∼ Beta
	dfβ	User specified (default value, 5)
	Sβ	Sβ ∼ Gamma
Scaled-t mixture (BayesB)	π (prop. of nonnull effects)	π ∼ Beta
	dfβ	User specified (default value, 5)
	Sβ	Sβ ∼ Gamma

^aFurther details are given in the supporting information (Section A of File S1).

^bThis approach is further discussed in de los Campos et al. (2009b).