The phrase "applied on the random" is not correct in standard written English.
It seems to be an attempt to convey a sense of randomness in application, but the phrasing is awkward and unclear.
Example: "The method was applied randomly to the selected samples."
Alternatives: "applied at random" or "applied randomly".
Significance of the age-related increases in total, familial, and individual variation was tested with a one-sided Z-test applied on the random effect estimates of age.
Significance of the age-related changes in variation or discordance was tested with a one-sided Z-test applied on the random effect estimate of age group, age, or sampling time divided by its SE, which adds up to a Wald test.
The followed approach is valid, since the eigenvalues extracted by V are applied on the Gaussian random variable z ∼ N 0, I LN.
The identification of the probabilistically dominant failure modes of complex structures and the estimation of their reliability can be reduced to the solution of an optimization problem in the standardized normal space of the variables that control the random loads applied on the structure and the random strengths of its members.
The EM algorithm is applied on the new sample with random reinitialization of the Gaussian components that are not fixed yet (the means are set to randomly chosen observations from the new sample).
An arbitrary threshold of 125 (non-specific staining level) was applied to the random selected area on the tissue as background.
Scanner normalization and random correction were applied on the data and the images were reconstructed with the standard EM iterative algorithm.
A stochastic description of the state evolution is represented by a stochastic process s: t ↦ s(t) defined on t ∈ I ⊂ R applied on the network state space, where I is an interval: for each time t ∈ I ⊂ R, s(t) represents a random variable applied on the network state space.
In short, the Random Forest algorithm was applied on ten random training datasets to select 25 markers with the highest rank of "importance" in the prediction of the origin of the strains (clinical or environmental).
A perturbation (according to the field described below) is applied on some random scattered trials (19%).
