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Re: Fitting: How does gnuplot calculate the covariance matrix?

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On 12.04.2011 11:28, Ingo Thies wrote:

> My concern here ist that you set the y-offsets of the error lines rather
> arbitrary.

Where do you think I did anything arbitrary?  The y offset of the fittet 
line is a result of the fit, including an error.  So constructing the 
error corridor has to include varying the fitted parameter "y offset" 
across it's fitted error range.

> This approach assumes that the errors are smallest at the
> lower end of the xrange, and largest at the upper end, since the error
> corridor always opens for larger x.

Yes, that's what this particular model function does.  That was your 
choice, not mine.  A different model, e.g. a*(x-x0), might yield a 
different behaviour.

> BTW Did you even look at the poster figure I have linked to, where I
> have done exactly this (for a small sample, however)?

For the context of this discussion, that poster figure is really quite 
meaningless.  It has neither the same data, nor the same model function 
as what we've been discussing.

>>> And along this 1-sigma contour a and b walk through
>>> the error intervals above.

>> So which parameters of the error ellipse did you give above: horizontal
>> and vertical section at the center, or overall size of the enclosed,
>> axis-aligned bounding box?
>
> All (a,b) at small steps around the ellipse.

A misunderstanding.  I was asking: where in that ellipse did those 
numbers your quote as errors of a and b come from?

> This may be true for a moderate number of samples. However, for large
> number of samples, as my colleague did, the error corridor is way too
> small. By nearly an order of magnitude or so.

Let's see some actual test case to demonstrate that.

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Thread

Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-08 13:05 +0200
  Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-08 17:18 +0200
    Re: Fitting: How does gnuplot calculate the covariance matrix? Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-04-10 19:31 +0200
      Re: Fitting: How does gnuplot calculate the covariance matrix? Charles Allen <ca137tmp@earthlink.net> - 2011-04-10 20:14 -0500
        Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-14 15:41 +0200
      Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-11 21:42 +0200
        Re: Fitting: How does gnuplot calculate the covariance matrix? Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-04-11 23:27 +0200
          Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-12 11:28 +0200
            Re: Fitting: How does gnuplot calculate the covariance matrix? Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-04-16 00:03 +0200
              Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-16 18:06 +0200
      Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-14 15:07 +0200
      Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-15 13:47 +0200
  Re: Fitting: How does gnuplot calculate the covariance matrix? Hans-Bernhard Bröker <HBBroeker@t-online.de> - 2011-04-10 19:04 +0200
    Re: Fitting: How does gnuplot calculate the covariance matrix? Ingo Thies <ingo.thies@gmx.de> - 2011-04-11 22:13 +0200

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