We expressed the variances at each level as a percentage of their contribution to the total variance from an initial model adjusting for age and gender only and from a final model accounting for all covariates.
The variance ratio expresses the variance of males in relation to that of females.
The next step is to express the variance of length of life (as an indicator of health),, in monetary units.
Also, the uncorrelation between quantization noises enables to express the variance of a summation of random variables as the summation of the variance of each random variable.
We then use the linearity of botharguments of the covariance bracket to express the variance of the quadratureoperator as S ϕ = ∫ − ∞ ∞ [ e i ϕ e − i ϕ ] G [ 〈 a ˜ ˆ i , a ˜ ˆ i 〉 〈 a ˜ ˆ i , a ˜ ˆ i † 〉 〈 a ˜ ˆ i † , a ˜ ˆ i 〉 〈 a ˜ ˆ i † , a ˜ ˆ i † 〉 ] × G T [ e i ϕ e − i ϕ ] d ω ′. (67).
The total order Sobol index describes the influence of the parameter itself plus all its combination with the other eight (total order SI is the sum of all SI of the variable, including higher order indices that express the variance of groups of variables).
If we express the variance in fractional terms, this becomes <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0002774.e026.PNG" class= inline-graphic"/> The universal noise model of Eq (1) corresponds to β = inline-graphicise) and b = αg0.
As an alternative, the budget constraint, equation (4), can be substituted into the objective function, equation (3), so as to get a new objective function, which expresses the variance as a function of only one variable, be it either n s or n d.
The S measures appear to be similar to the measure of distance between covariance matrices used by Mitteroecker and Bookstein [ 33], based on the calculation of relative eigenvalues, i.e., the eigenvalues of the product of one matrix premultiplied by the inverse of the second matrix, and therefore on expressing the variances and covariances of one sample relative to those of the other sample.
Mean square error of prediction (MSEP) indicates expected squared Euclidian distance between predicted and observed phenotypes, R expressed the proportion of variance explained by the model and Q evaluates the prediction quality of the model.
