scaleMeanVarCurveRobust underlies other interface functions for
estimating the variance ratio factor of an unadjusted mean-variance curve
(or a set of unadjusted mean-variance curves)
in a robust manner.
scaleMeanVarCurveRobust(
z,
m,
d0,
p_low = 0.01,
p_up = 0.1,
nw = gauss.quad(128, kind = "legendre")
)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 could be robustly estimated by estimateD0Robust.
Lower- and upper-tail probabilities for Winsorizing the
FZ statistics associated with each bioCond.
A list containing nodes and weights variables for
calculating the definite integral of a function f over the
interval [-1, 1], which is approximated by
sum(nw$weights * f(nw$nodes)). By default,
a set of Gauss-Legendre nodes along with the corresponding weights
calculated by gauss.quad is used.
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 derive a robust estimation of log variance ratio factor by
Winsorizing the FZ statistics of each bioCond and matching the
resulting sample mean with the theoretical expectation of the Winsorized
distribution, which is calculated by using numerical integration (see
also "References").
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.
Finally, we get an estimate of variance ratio factor by taking an exponential.
Phipson, B., et al., Robust Hyperparameter Estimation Protects against Hypervariable Genes and Improves Power to Detect Differential Expression. Annals of Applied Statistics, 2016. 10(2): p. 946-963.
bioCond for creating a bioCond object;
fitMeanVarCurve for fitting a mean-variance curve;
varRatio for a formal description of variance ratio
factor; estimateD0Robust
for estimating the number of prior degrees of freedom associated with
a mean-variance curve (or a set of curves) in a robust manner;
estimatePriorDfRobust for an interface to robustly
estimating the number of prior degrees of freedom on bioCond
objects as well as robustly adjusting their mean-variance
curve(s) accordingly.
estimateD0 and scaleMeanVarCurve
for the ordinary (non-robust) routines for estimating number of prior
degrees of freedom and variance ratio factor, respectively.
# Refer to "Examples" given in the help page for the function
# estimateD0Robust.
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