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

Robert Kern robert.kern@gmail....
Thu Mar 24 11:09:33 CDT 2011


On Thu, Mar 24, 2011 at 10:33, Daniel Mader
<danielstefanmader@googlemail.com> wrote:
> Hi,
>
> this is not a software question or scipy problem but rather I have no
> clue how to tackle this on a mathematical level.
>
> I'd like to create a unique fit function for data. Attached is a file
> which holds three measurements for three different known
> concentrations, i.e. my "calibration" measurement at low, medium and
> high concentration.
>
> Apparently, the temperature behavior of the chemical reaction is
> exponential, i.e. the photon yield increases with about 10%/K for the
> examined range for a given concentration.

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.

> 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.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
  -- Umberto Eco


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