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At the next level of hierarchy, uniform hyper-priors (i.e. (Uleft( {0,10} right))) were assigned to the variance parameters ((sigma_{w}^{2}), (sigma_{u}^{2})).
To test the robustness of the model results in the present study, different fixed values were assigned to the variance.
Scaled inverse chi-square distributions were assigned to the variance parameters σ ε 2 and σ α 2, each with 3 degrees of freedom and a scale parameter equal to 1.
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Bayes A is also highly dependent on the prior distribution assigned to the variances of regression coefficients.
For j in {1, … , p} update the variance of marker effects with a draw from a scaled-inverse chi-square density with scale and degree of freedom parameters β j 2 + d. f. β × S β and 1 + d. f. β, respectively, where S β and d. f. β are the prior scale and prior degree of freedom assigned to the variances of marker effects.
Thus, when paternally inherited effects are ignored in the estimation model, its variance is assigned to the remaining variance components in order to accommodate the observed correlations between relatives.
Marker effects are assumed independent and identically distributed a priori, whereas the distribution assigned to (the prior variance of marker effects) and (the prior of residual variance) is χ−2 df, s) (for example, de los Campos et al., 2012).
S0, df0, R2 (numeric) define the prior assigned to the residual variance, df0 defines the degrees of freedom, and S0 defines the scale.
Here, S ε and d. f. ε are the prior scale and prior degree of freedom assigned to the residual variance and { ε i = y i − μ − ∑ j = 1 p x i j β j } are the current model residuals.
Stated the other way around, the existence of paternally inherited variation that is not accounted for by the maternal model will tend to be assigned to the remaining variance components according to Equation (1) in order to accommodate the observed correlations between relatives.
Model SD assigned most of the genetic variance to paternal gametic effects, although negligible amounts of variability were also assigned to the gametic maternal variance component.
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