Figure 1.
Figure 1.

Gaussian and Double-Exponential densities, both for a random variable with zero mean and unit variance.

 


Figure 2.
Figure 2.

Realized marker effects.

 


Figure 3.
Figure 3.

Prior density of λ when λ2 is assigned a gamma prior with rate equal to 2 × 10−5 and shape equal to 0.52. When λ2G(r,δ), ; this is the density displayed above.

 


Figure 4.
Figure 4.

Prior and estimated posterior density of the residual variance, by model (BRR = Bayesian Ridge Regression; BL = Bayesian LASSO).

 


Figure 5.
Figure 5.

Estimates of marker effects (left panel) and of genetic values (right panel) obtained with the Bayesian Ridge Regression (BRR, vertical axis) versus those obtained with the Bayesian LASSO (BL, horizontal axis).

 


Figure 6.
Figure 6.

R-code used to fit models of example 2.

 


Figure 7.
Figure 7.

Predictive mean squared error (PMS, vertical axis) versus values of the regularization parameter of the Bayesian LASSO (horizontal axis), by environment. The vertical and horizontal dashed lines give the average (across 10 folds of the cross-validation) estimated posterior mean of λ and the estimated PMSE obtained when a prior was assigned to λ.