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In (3), ρ is a selected threshold for reducing the noisy effect and should be proportional to I(p). Figure 3 shows how trinary census works well under noise environments.
Considering geographic location as a random effect controls for possible pseudo-replication (i.e., multiple samples from the same site) and the noisy effect of site-to-site variation in sample sizes [27].
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Based on the results provided by Table 4 and Fig. 5, it can be concluded that our proposed orthogonal moments are less sensitive to the noisy effects.
It is clear from Figs. 7 and 8 that the relative error rate is very low (10−10), which indicates that the proposed moment invariants exhibit good performance and express high numerical stability under different geometric transformations, as well as in presence of noisy effects.
We expected that some estimated QTL main effects and Q×E interaction effects might be detected by chance and thus wanted to exclude the noisy effects.
The reason is that the MLM assumes that all the SNPs have effect on the phenotype, including those SNPs with small or noisy effects.
Therefore, obtained by MLM would include both "significant" and "noisy" effects and thus lead to overestimation of PVE according to (3).
In practice, many SNPs might have very small/noisy effects on the complex traits [ 10 ]; hence, we are simulating those scenarios with letting some of the SNPs have noisy effects on the phenotype that are normally distributed with a very small variance.
The reason is that the MLM can not distinguish the "significant" SNP effects versus those "noisy" effects due to its assumption that all random effects follow the same distribution.
In order to investigate temporal regularity (Regular vs. Irregular) and noise level (Silent vs. Noisy) effects, we used four different conditions: regular sequencing in silence (Regular_Silent), irregular sequencing in silence (Irregular_Silent), regular sequencing in noise (Regular_Noisy), and irregular sequencing in noise (Irregular_Noisy).
Another tack would be to use prices to separate quiet and noisy passengers in effect, creating a market for silence.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com