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Old 07-08-2015, 07:56 AM   #4
Michael Love
Senior Member
Location: Boston

Join Date: Jul 2013
Posts: 333

There is a theoretical justification. The sum of Poisson RVs (random variables) is Poisson. Raw counts of uniquely assigned reads to genes are very close to Poisson distribution across technical replicates. And the statistical model includes Poisson RVs or RVs with higher dispersion (due to biological variation). So the sum is a good idea for summarizing technical replicates.

Note that the average of Poissons is not Poisson, for example, it has less variance than the mean. Suppose we take the mean of 5 Poisson RVs with lambda=10 and call this new thing X. The expected value will be 10,

> mean(replicate(1000, mean(rpois(5, lambda=10))))
[1] 9.9804

but the variance of X is now less than the mean:

> var(replicate(1000, mean(rpois(5, lambda=10))))
[1] 1.951687

This kind of a RV, a count which is under-dispersed, is not possible to model with the count-based methods.
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