[SciPy-User] technical question: normed exponential fit for data?

[josef.pktd at gmail.com]

On Thu, Mar 24, 2011 at 1:19 PM, Daniel Mader
<danielstefanmader at googlemail.com> wrote:
> Hi,
>
>> Hmm. I certainly wouldn't have come to that conclusion looking at the
>> data. At least for #0 (high concentration?), the linear fit is
>> substantially better.
>
> yes, of course, there is always a better fit possible, no doubt. When
> I perform a fit for only a single data series, I can optimize both c0
> and c1 in the equation:
>  f(x) = c[0] * scipy.exp(c[1]*x)

what I would do use loglinear specification, the error looks
increasing for larger counts. use a factor encoding for the
concentration that allows for different intercepts, constrain c[1] to
be the same for all observations.

log(f(x)) = c0 * dL + c1*dM + c2*dH + c3*x

dL, dM, dH are dummy variables, that are 1 if the observation has L
(or M or H) concentration and 0 for the other concentration.

run a linear regression on this, and run some tests to see whether the
assumptions look ok.

Josef


>
> It is just my observation that with a factor c[1]=0.1 the fit works
> very well for a broad range of concentrations.
>
> However, c[0] needs to be different, and that is my problem. Can I
> somehow normalize the measurement values in order to compensate for
> different temperatures?
>
>>> Now comes the tricky part: I'd like to use this knowledge for a
>>> temperature compensation because I only need to determine the
>>> concentration. The temperature of the reaction is measured
>>> simultaneously but might vary in the range of +-3K. In terms of assay
>>> performance, that makes a huge difference due to the 10%/K so that I'd
>>> need to compensate for it.
>>>
>>> How can I use my calibration measurement to find a function which I
>>> could use to compensate for varying temperatures?
>>
>> Can you do more calibrations with different concentrations? For any
>> given temperature, you essentially only have three data points with
>> which to determine the relationship between concentration and photon
>> count. That's pretty difficult without any theory to help you fill in
>> the gaps.
>
> These experiments are very expensive, a single series from above is
> about 300€. So, I was hoping there is something I can learn from these
> already. It needs not be perfect, a procedure outline would be nice so
> that I could justify to spend even more money on this.
>
> But, as stated above, right now I only have a "feeling" that I can do
> something about it but it's still hidden in the mist...
>
> Thanks for taking the time to think about it!
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