[BioC] RMA-bimodality:

[Wolfgang Huber]

Hi Peter,

- doesn't the distribution of mRNA abundances (i.e. physical
concentrations measured e.g. in average no. of molecules per cell) span
the whole range from just undetectably above zero to very large? I am
not sure what mechanism would then result in two distinct peaks of
fluorescences, one for "absent" and and one for "present" mRNAs.

- I tried find a definition of "truely unimodal distributions" (and I
suppose, "falsely unimodal distributions"), but couldn't find one, can
you advise?

Cheers
 Wolfgang

Peter G. Warren wrote:
> 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.
> 
> Regards,
> - 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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Wolfgang Huber  EBI/EMBL  Cambridge UK  http://www.ebi.ac.uk/huber