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However, in practical problems the parameters of distribution are unknown and can only be estimated from random samples.
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For each of the five populations, relationship matrices were estimated from random subsets of markers, with the shrinkage intensity chosen to minimize the expected MSE.
The background signal within coding regions thus has to be estimated from a random model that takes the protein coding nature of the sequence into account.
Computationally, the sum of d × Δpref can serve as a proxy for a correlation or regression coefficient; therefore, 1-tailed statistical significance can be estimated from the proportion of random permutations of d vs. Δpref that lead to a higher sum of products.
These approaches have the benefit of allowing contamination levels to be estimated from relatively small sets of random sequences.
Although chance DNA similarity between pairs of unrelated individuals is tiny (< 2%), overall genetic influence, or GCTA-based heritability, can be estimated from the extent to which this random DNA similarity predicts their phenotypic similarity.
For larger data sets, the true fraction of trees for which the taxon coverage is decisive can be estimated from the fraction in a large random sample of trees (under a uniform/equiprobable distribution of trees).
The number of correlate pairs measured in this analysis was too many to readily assess for estimation of q values, so q values were estimated from ten random samplings of the gene expression and GI50 data sets.
The mean values and variances of the quality characteristics in the first and second stages and the residuals are estimated from the random samples and then the process capability indices are calculated.
The reliability of each node was estimated from 100 random bootstrap resamplings of the data.
The reliability of each node was estimated from 1000 random bootstrap resamplings of the data.
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