In this case, trait i is the "discovery" sample.
To quantify the proportion of genes whose expression is associated with each pair of AD traits, the following procedure was used: for each trait i, we used the 0.05 FDR threshold to identify genes whose expression associate with trait i.
In summary, element (i,j) in this figure represents the pi1 statistic when assessing the 0.05 FDR genes (identified in the discovery sample) from trait i (rows) in the replication sample (trait j)(columns).
Likewise, X Ti =0 if a male has trait i, and 0 if he does not.
We model each λ ij (specifying how observed trait i is related to latent trait j) with a normal distribution.
Note that a red square in the i-th row and j-th column indicates that trait i causally affects trait j.
The expectation of y i (i = 1 to 5 and ≥ 6) is X i β i and the variance-covariance structure of random effects was assumed to be: where and are the direct additive genetic and residual variances for trait i, respectively, is the direct genetic covariance between trait i and j (j = 1 to 5 and ≥ 6) and their residual covariance.
From the latent variable model, the residual variance for trait i is ∑ k r k, i 2 + τ e i 2, and the residual covariance between traits i and j is ∑ k r k, i r k, j.
We represented the dynamics supported on a network P through a matrix π, where π i,n describes the probability that acquisition of trait i occurs at the nth step in an evolutionary trajectory.
Denote f c i MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGMbGzdaqhaaWcbaGaem4yamgabaGaemyAaKgaaaaa@30D8@ is the relative fecundity of a male belonging to the cth class of a given trait i.
The conditional posterior of the factor loading precision parameter φ ij for trait i on factor j is π (φ i j | τ j, λ i j ) ∼ Ga (ν + 1 2, ν + τ j λ i j 2 2 ).
