[proFit-list] feature request--calculate-Data Transform with errors

[perego]

If one wishes to get a true estimate of confidence levels for the "y- 
values" of a fitted function at a given point x,
it might prove complicated enough (the only method that comes to my  
mind now would be analyzing the
situation with a Monte-Carlo simulation). Nevertheless, for an  
estimate of the variance of the y-value,
the general error-propagation formula might be used. Let's say your  
fitted function is y=f(x,a1,a2... ar) where
a1 ... ar are the fitted parameters. The variance estimate for y would  
be given by the matrix product M C Mt
where:
- C is the covariance matrix {r x r} of the parameters a1 ... ar,  
whose elements can be obtained from the proFit engine by calling  
GetResult(covariance...).
If also x has an associated error C can become a {r+1 x r+1} matrix  
whose first row and column have the squared error for x as first  
element and r null elements
(I'd say that, in general, your x value and the fitted parameters are  
mutually independent)
- M is the matrix that represents the linearized relationship between  
(x,a1,... ar) and y. In this case, it reduces to a row vector  
containing the
partial derivatives df/dx, df/da1 ... df/dar calculated at the given  
point. Mt is the transposed of M.

Best regards
Andrea

On Aug 14, 2008, at 4:47 PM, Andrew Calvert wrote:

> I frequently fit standard data with polynomials (2nd or 3rd order),
> and then interpolate intervening values.  I fet the data then
> interpolate those using Calc>>Data Transform..., select the Various
> Functions button and calculate with Y = Polynomial(x).  I would like
> to use the error that profit calculates to add an error column.
> Ideally this would be Y = ±Polynomial(x).
>
> Alternatively, I could probably write a function, but this might be
> helpful for others.
>
> Thanks, Andy
> ____________
> Andrew Calvert
> Volcano Hazards Team
> US Geological Survey
> 345 Middlefield Road, MS-937
> Menlo Park, CA 94025
> 650-329-5276 office
> 650-329-4664 fax
> acalvert at usgs.gov
>
>
>
>
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