scaleMeanVarCurve underlies other interface functions for estimating
the variance ratio factor of an unadjusted mean-variance curve (or a set of
unadjusted mean-variance curves).
scaleMeanVarCurve(z, m, d0)The estimated variance ratio factor for adjusting the mean-variance
curve(s). Note that the function returns NA if there are not
sufficient genomic intervals for estimating it.
A list of which each element is a vector of FZ statistics
corresponding to a bioCond object (see also "Details").
A vector of numbers of replicates in bioCond
objects. Must correspond to z one by one in the same
order.
A positive real specifying the number of
prior degrees of freedom of the
mean-variance curve(s). Inf is allowed. Note that d0 is
typically estimated via estimateD0.
For each bioCond object with replicate samples, a vector of
FZ statistics can be deduced from the unadjusted mean-variance curve
associated with it. More specifically, for each genomic interval in a
bioCond with replicate samples, its FZ statistic is defined to be
\(log(t_hat / v0)\), where \(t_hat\) is the observed variance of signal
intensities of the interval, and \(v0\) is the interval's prior variance
read from the corresponding mean-variance curve.
Theoretically, each FZ statistic follows a scaled Fisher's Z distribution
plus a constant (since the mean-variance curve is not adjusted yet), and we
can use the sample mean (plus a constant that depends on the number of
prior degrees
of freedom) of the FZ statistics of each single bioCond to get
an estimate of log variance ratio factor.
The final estimate of log variance ratio factor is a weighted mean of
estimates across bioCond objects, with the weights being their
respective numbers of genomic intervals that are used to calculate
FZ statistics.
This should be appropriate, as Fisher's Z distribution is roughly normal
(see also "References"). The weighted mean is actually a plain (unweighted)
mean across all the involved genomic intervals.
Finally, we get an estimate of variance ratio factor by taking an exponential.
Smyth, G.K., Linear models and empirical bayes methods for assessing differential expression in microarray experiments. Stat Appl Genet Mol Biol, 2004. 3: p. Article3.
Tu, S., et al., MAnorm2 for quantitatively comparing groups of ChIP-seq samples. Genome Res, 2021. 31(1): p. 131-145.
bioCond for creating a bioCond object;
fitMeanVarCurve for fitting a mean-variance curve;
varRatio for a formal description of variance ratio
factor; estimateD0 for estimating the number of prior
degrees of freedom associated with a mean-variance curve (or a set
of curves); estimatePriorDf for an interface to
estimating the number of prior degrees of freedom on bioCond
objects as well as adjusting their mean-variance curve(s) accordingly.
estimateD0Robust and scaleMeanVarCurveRobust
for estimating number of prior degrees of freedom and variance ratio
factor in a robust manner, respectively.