Re: problem with NonlinearFit
- To: mathgroup at smc.vnet.net
- Subject: [mg4788] Re: problem with NonlinearFit
- From: rubin at msu.edu (Paul A. Rubin)
- Date: Mon, 16 Sep 1996 23:51:17 -0400
- Organization: Michigan State University
- Sender: owner-wri-mathgroup at wolfram.com
In article <508n6c$com at dragonfly.wolfram.com>,
"Brian O'NEILL" <oneill at iiasa.ac.at> wrote:
->
->I am having the following problem with the NonlinearFit function, and
would
->appreciate any tips you might have. (I have appended sample Mathematica
code
->below.)
->
->My goal is to fit a non-monotically decreasing time series with a
->monotonically decreasing function (specifically, a sum of decaying
->exponenitials plus a constant). I am approaching the problem by using
->NonlinearFit and specifying a general functional form, then attempting to
->constrain the search to non-negative coefficients and non-positive
->exponents. However, in general I have run into the following problems:
->
->(1) NonlinearFit will accept parameter specifications of the form {x,xo},
or
->of the form {x,minx,maxx}, but not of the form {x,xo,xmin,xmax}. This
means
->I can constrain the variables, but I can't start from different points to
->test robustness.
->
->(2)The routine stops when it tries to search outside the constraints
instead
->of continuing the search in a different direction, so that it is
important
->to be able to specify different initial values to look elsewhere.
->
[remainder edited out]
a. I think you've hit on a bug in NonlinearFit, or more precisely a
discrepancy between the documentation in the "Guide to Standard Mma
Packages" and the actual function (at least according to what
??NonlinearFit returns).
b. This is tacky, but it might function as a workaround: replace a1, a2,
a3, tau1, tau2, tau3 with a1^2, a2^2, ... and then don't constrain a1, ...,
tau3. Presumably you can fiddle with starting values, then.
c. WAY BACK WHEN I was a grad student (in math), I worked for a prof once
who was interested in a technique called "exponential peeling" for fitting
precisely this kind of function (sum of decaying exponentials) to data.
I've forgotten the details, but I think it was a successive approximation
scheme, which started by assuming that for large values of t the term with
the smallest decay rate would dominate; so you estimated that term out in
the tail, subtracted it from the data, recursed at it until you'd estimated
all the terms, then started over (or something like that - it has been a
while). If that method hasn't been discredited in the last century or so,
you might want to look it up.
-- Paul
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