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How do you calculate variance stabilizing transformation?
General method for finding variance-stabilizing transformations: If Y has mean µ and variance σ2, and if U = f(Y), then by the first order Taylor approximation, U ≈ f(µ) + (Y – µ) f'(µ), so Var(U) ≈ Var[f(µ) + (Y – µ) f'(µ)] = [f'(µ)]2Var(Y – µ) = [f'(µ)]2σ2.
What happens to the variance when you multiply every data point by a constant?
The variance of a constant is zero. Rule 2. Adding a constant value, c, to a random variable does not change the variance, because the expectation (mean) increases by the same amount. Multiplying a random variable by a constant increases the variance by the square of the constant.
What is variance equal to?
The variance (σ2), is defined as the sum of the squared distances of each term in the distribution from the mean (μ), divided by the number of terms in the distribution (N). From this, you subtract the square of the mean (μ2). It’s a lot less work to calculate the standard deviation this way.
Which is the best transformation for variance stabilizition?
This results in the variance stabilizition to be only approximate. The more the size factors differ, the more residual dependence of the variance on the mean will be found in the transformed data. rlog is a transformation which can perform better in these cases.
How does the variancestabilizingtransformation function ( VST ) work?
This function calculates a variance stabilizing transformation (VST) from the fitted dispersion-mean relation (s) and then transforms the count data (normalized by division by the size factors or normalization factors), yielding a matrix of values which are now approximately homoskedastic (having constant variance along the range of mean values).
When is the variance stabilizing transformation called logarithmic?
If X is a positive random variable and the variance is given as h(μ) = s2μ2 then the standard deviation is proportional to the mean, which is called fixed relative error. In this case, the variance-stabilizing transformation is. That is, the variance-stabilizing transformation is the logarithmic transformation.
How is the variance of a deseqtransform calculated?
Note that for DESeqTransform output, the matrix of transformed values is stored in assay (vsd) . getVarianceStabilizedData also returns a matrix. For each sample (i.e., column of counts (dds)), the full variance function is calculated from the raw variance (by scaling according to the size factor and adding the shot noise).