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Question: Asymptotic dispersion, DESeq2
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gravatar for stevenn.volant
22 months ago by
stevenn.volant0 wrote:

Hi,

Does someone have any idea about the asymptotic behavior (i.e. with a large number of samples) of the dispersion estimation ?

Thank you

ADD COMMENTlink modified 22 months ago by Michael Love15k • written 22 months ago by stevenn.volant0
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gravatar for Michael Love
22 months ago by
Michael Love15k
United States
Michael Love15k wrote:

DESeq2's estimator is the posterior mode. This converges to the unbiased 'maximum of the Cox-Reid adjusted likelihood' estimator as the sample size grows to infinity (see DESeq2 paper's Methods section, which has reference to the edgeR paper on this adjustment).

Keep in mind that, like the sample variance, the MLE for the dispersion takes longer to converge to the true value compared to estimators for the mean. Which is why sharing information across genes (using the prior distribution for genes with similar mean value) is such a good idea and improves inference.

Here's a toy example and a plot showing the posterior mode converging to the true value (orange) although it starts around the center of the prior (purple).

 

library(DESeq2)
samp.size <- c(3:12,
               2:10 * 10,
               5:12 * 25)
disps <- numeric(length(samp.size))
prior.mean <- .2
true.disp <- .1
for (i in seq_along(samp.size)) {
  cat(i)
  dds <- makeExampleDESeqDataSet(n=100, m=samp.size[i],
                                 dispMeanRel=function(x) prior.mean)
  cnts <- rnbinom(ncol(dds), mu=200, size=1/true.disp)
  mode(cnts) <- "integer"
  counts(dds)[1,] <- cnts
  sizeFactors(dds) <- rep(1, ncol(dds))
  dds <- estimateDispersions(dds, quiet=TRUE, fitType="mean")
  disps[i] <- dispersions(dds)[1]
}
plot(samp.size, disps, log="y")
abline(h=prior.mean, col="purple")
abline(h=true.disp, col="orange")

 

ADD COMMENTlink modified 22 months ago • written 22 months ago by Michael Love15k
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