[BioC] RMA-bimodality:

Peter G. Warren peter.warren at verizon.net
Tue Jun 6 17:54:37 CEST 2006

Hi, Wolfgang, Noel,

It is true that a non-linear transformation can change the number of nodes
of the data, and that that transformation can be sufficient to explain the
bimodality we see in background-corrected data. However, in my experience,
the raw probe-level data is itself bimodal. When there is some real signal
present, the probe-level intensities are actually from two different
distributions. The first ("absent") is where there is no positive transcript
binding, only cross-hyb, non-specific binding, and background. The second
("present") is all that, plus true target transcript binding. This
bimodality is more evident with log-transformed values. (In contrast, a
log-transformation of a truly unimodal distribution, such as
density(rnorm(...), is still unimodal.) In every case I've looked at, the
"absent" distribution dwarfs the "present" one, so it often looks like one
mode, before log transformation. After log transformation, I have been
unable to model the data successfully with a single distribution; it always
takes two.

- Peter Warren

> Hi Noel,
> > Just so that I am clear- the point is that the
> > bimodality is not an artifact of the convolution, but
> > simply the fact that the number of modes of a
> > distribution is not conserved under monotonous
> > transformations.
> No, I did not say that, and I do not know how to understand 
> this sentence,
> since "the convolution" is directly related to "the monotonous
> transformation" that we are talking about
> > This is why the paper points to the
> > fact that the histograms of log2 (PMs/MMs) stratified
> > by log2(PMs) is bimodal
> I leave the exegesis of the paper to its authors.
> > -so bimodality is a more
> > general property of the probe level data.
> As you have just said yourself, the number of modes is not a 
> property of
> the data, but of the data plus the particular (non-linear) 
> transformation
> that you choose to apply to them.
> Best wishes
>  Wolfgang.

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