<p>Many experts claim that the negative binomial distribution is better than the Poisson distribution for modeling discrete RNA-Seq data.</p>

<p>Is this because </p>

<ul>
<li>The expression profiles of organisms resemble the negative binomial distribution - i.e.if I binned real gene transcription counts from an RNA-Seq experiment it would look like the plot below. </li>
</ul>

<p>or</p>

<ul>
<li>The sampling error of gene expression is such that the true population mean of a gene looks like the negative binomial - i.e the true mean expression level of that gene is probably more (because of the skew) than the mean expression level of a sample of reads of that gene drawn from replicates.</li>
</ul>

<p>or are these two concepts the same thing? </p>

<p><img src='http://zoonek2.free.fr/UNIX/48_R/g579.png' alt='alt text' /></p>

<p>It's not about the skew of the distribution, it's about the variance. Take a look at the top two panels of <a href="http://www.plosone.org/article/slideshow.action?uri=info:doi/10.1371/journal.pone.0016327&amp;imageURI=info:doi/10.1371/journal.pone.0016327.g001">this image</a> (self link).  The big difference is that the distribution based on a NB distribution can be shorter and fatter, or overdispersed.</p>

<p>The key to understanding the negative binomial distribution is that it's the same as taking lots of poisson distributions with slightly different means and adding them together. Essentially, this is saying that there's some sort of bias in the data causing this variability, but we aren't sure exactly what's causing it. The obvious candidates (GC content, mapability, sequence composition, etc) don't explain it all. Since it's difficult to correct for something when we don't know the source, we can do the next best thing, which is to model the distribution we see accurately. That's where NB distributions can overcome some of the limitations of poisson (namely that the variance/mean ratio is always equal to one).</p>
