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R(k) can be computed from samples of x c (t) taken at an arbitrarily lower rate using nested or coprime sparse sampling.
For the Bayesian analysis, the posterior mean TLI can be computed from samples of the posterior distribution.
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Posterior probabilities of nodes were computed from sampled trees after burn-in.
The miRNA expression levels (Additional file 3) were computed from sample-paired TCGA small RNA-seq data using a previously described small RNA-seq analysis pipeline [ 30].
As detailed in the Methods section, the technique we have developed here, although admittedly simple, can be used in other contexts, where a given number of clustering solutions must be computed from different samples of the same dataset.
The highest density interval of can be computed from the sample by using the emp.hpd function in the R package TeachingDemos.
Then, the conditional mean for its genomic EBV is, where is the posterior mean of α, which can be computed from the MCMC samples.
They can be computed from large genotype sample sets, such as those from the HapMap project, or from a genome-wide association (GWA) study by plotting the matrix of association values for each pair of SNPs.
In practice, however, sample co-expression networks are usually smaller than gene co-expression networks, but the edges in sample co-expression networks may be computed from very high-dimensional data, since each sample is described by thousands of genes.
The numerical case studies are conducted as follows: Π and C are randomly sampled; the derived random quantities r and s are computed from the samples.
The ensemble-averaged PSDF in the turbulent flame is computed from individual samples of the PSDF from large sets of Lagrangian trajectories.
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