estimateD0: Workhorse Function for Estimating Number of Prior Degrees of...

In MAnorm2: Tools for Normalizing and Comparing ChIP-seq Samples

Workhorse Function for Estimating Number of Prior Degrees of Freedom

Description

estimateD0 underlies other interface functions for assessing the goodness of fit of an unadjusted mean-variance curve (or a set of unadjusted mean-variance curves).

Usage

estimateD0(z, m)

Arguments

z	A list of which each element is a vector of FZ statistics corresponding to a bioCond object (see also "Details").
m	A vector of numbers of replicates in bioCond objects. Must correspond to z one by one in the same order.

Details

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 variance (plus a constant) of the FZ statistics of each single bioCond to get an estimate of trigamma(d0 / 2), where d0 is the number of prior degrees of freedom (see also trigamma).

The final estimate of trigamma(d0 / 2) is a weighted mean of estimates across bioCond objects, with the weights being their respective numbers of genomic intervals minus 1 that are used to deduce the FZ statistics. This should be appropriate, as Fisher's Z distribution is roughly normal (see also "References"). The weighted mean is similar to the pooled sample variance in an ANOVA analysis.

Finally, an estimate of d0 can be obtained by taking the inverse of trigamma function, which is achieved by applying Newton iteration to it. Note that d0 is considered to be infinite if the estimated trigamma(d0 / 2) is less than or equal to 0.

Value

The estimated number of prior degrees of freedom. Note that the function returns NA if there are not sufficient genomic intervals for estimating it.

References

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.

See Also

bioCond for creating a bioCond object; fitMeanVarCurve for fitting a mean-variance curve; estimatePriorDf for an interface to estimating the number of prior degrees of freedom on bioCond objects; varRatio for a description of variance ratio factor; scaleMeanVarCurve for estimating the variance ratio factor for adjusting a mean-variance curve (or a set of curves).

estimateD0Robust and scaleMeanVarCurveRobust for estimating number of prior degrees of freedom and variance ratio factor in a robust manner, respectively.

MAnorm2 documentation built on Oct. 29, 2022, 1:12 a.m.