Specifically, we apply a matrix of means and standard deviations from the complete Iceland data.
The resulting matrix of means was subjected to principal components analysis to capture the correlations among variable means in a more manageable number of dimensions (Figure 6).
We suppose that all intensities are independent random variables with distribution (1) Y i, j ∼ p (· ; μ i, j ), μ i, j = E (Y i, j ) where the matrix of means (μ i, j ) 1 ≤ i ≤ j ≤ n is an upper triangular block diagonal matrix.
[ is a matrix of mean values, not the cell-specific methylation matrix.] As the variance of a beta-distributed variable with mean μ scales by, we obtain a matrix of mean-standardized errors by dividing each element of by, where is the corresponding element of.
Occupational, non-occupational, music, and home and other miscellaneous activities were each assigned noise levels derived from a matrix of mean exposures derived from peer-reviewed publications [ 26] (Additional file 1: Table S1).
Species positions in morphological space was quantified with a principal component analysis (PCA) using the R package Ade4 [ 32] based on the covariance matrix of mean values for each species.
Overall, hierarchical clustering of treatments based on their biological process signatures, and spectral clustering of GO terms based on semantic similarity enabled us to condense the initial 76 × 22 enrichment score matrix to a 13 × 5 matrix of mean enrichment scores.
This requires validation 'data' which, for a paternal half-sib design, can be summarized as the matrices of mean squares and cross-products between (M B) and within (M W) sires, as from an analysis of variance.
First, as a sanity check, we compared the accuracy of our method to a methods of moments estimate of G calculated as Gm = 4(B − W)/ n, where B and W are the between- and within-sire matrices of mean squares and cross products and n is the number of offspring per sire.
Again this is the matrix of class means, whose element, μ i, k, represents the mean of gene i across samples belonging to class k.
Given two groups, g 1 and g 2 respectively characterized by n 1 + n 2 = n observations, in order to test that the means of k variables are 0, let μ 1 be a 1 × k matrix of the means of the variables in g 1, μ 2 a 1 × k matrix of the means of the variables in g 2 and Σ be the estimated covariance matrix.
