URL:
<http://gna.org/task/?7824>
Summary: Model parameter ERROR estimation from Jacobian and
Co-variance matrix of dispersion models.
Project: relax
Submitted by: tlinnet
Submitted on: Mon 01 Sep 2014 02:31:47 PM UTC
Should Start On: Mon 01 Sep 2014 12:00:00 AM UTC
Should be Finished on: Mon 01 Sep 2014 12:00:00 AM UTC
Category: relax's source code
Priority: 3 - Low
Status: In Progress
Percent Complete: 0%
Assigned to: tlinnet
Open/Closed: Open
Discussion Lock: Any
Effort: 0.00
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Details:
In theory, one can get the Model parameter ERROR, from Jacobian and
Co-variance matrix of dispersion models.
The error of the dispersion points R2eff, stems from error on signal
intensity.
The R2eff and error points are used in the dispersion models.
If one knows the derivative of a function, one can get the estimated errors as
well.
http://www.orbitals.com/self/least/least.htm
This could get compared to a large number of Monte-Carlo simulations.
I relax, Monte-Carlo simulations are made by assuming an gaussian distribution
of R2eff points.
Estimating the errors from the Jacobian, is essential the same, since the
Co-variance matrix is made by populating the weight matrix with the R2eff
errors.
Therefore, the end result should in principle be the same.
The Jacobian matrix are easy to derive for the analytical models.
For the numerical solutions, it is a little different, since we then need to
take the derivative of a matrix. That can get tricky. In this situation, a
numerical gradient solution would probably be better.
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[task #7824] Model parameter ERROR estimation from Jacobian and Co-variance matrix of dispersion models.