Re: The standard deviation of Three fitting parameters is bigger than

• To: mathgroup at smc.vnet.net
• Subject: [mg100379] Re: The standard deviation of Three fitting parameters is bigger than
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Tue, 2 Jun 2009 06:44:13 -0400 (EDT)
• References: <h00d2t\$pkd\$1@smc.vnet.net>

```FindFit is not guaranteed to find a globally optimal fit, just
locally.

You can try various Methods for FindFit which are listed in tutorial/
UnconstrainedOptimizationIntroductionLocalMinimization

In addition the Method->NMinimize can be used which is supposed to
give you more globally optimal fits.

Often, I construct a Manipulate function which with I fit the function
interactively to my data (the sliders of the Manipulate are the
parameters of the model). I use the values I obtain in that way as the
starting values for the automatic fit.

Cheers -- Sjoerd

On Jun 1, 1:12 pm, holy... at gmail.com wrote:
> I try to fit a formula,
> 0.00138 t + 74.830*(t/a)^3*Integrate[(E^x x^4)/(E^x - 1)^2, {x, 0, a/
> t}] + n 3*8.314 (w/ t)^2 E^(w/ t)/(-1 + E^(w/t) )^2
> a,w,n are fitting parameters
> t is indenpendt veriable
>
> First, I let a=375.362 to fit w and n.
> FindFit[dataAl210K, {0.00138 t + 74.830*(t/375.362)^3*Integrate[(E^x
> x^4)/(E^x - 1)^2, {x, 0, 375.362/t}] + n 3*8.314 (w/ t)^2 E^(w/ t)/(-1
> + E^(w/t) )^2}, {n, w},t]
> I got {n -> 0.152124, w -> 1043.57} and the S.D.=0.150984 (standard
> deviation)
>
> Then, I relax these there fitting parameters and give initial
> conditions.
> FindFit[dataAl210K, {0.00138 t + 74.830*(t/a)^3*NIntegrate[(E^x x^4)/
> (E^x - 1)^2, {x, 0, a/t}]
> +n 3*8.314 (w/ t)^2 E^(w/ t)/(-1 + E^(w/t) )^2, {n > 0, a > 0, w >
> 0}}, {{n, 0.15}, {a, 375}, {w, 1043}}, t]
> Intuitively, the S.D. of three parameters should be smaller than two.
> However, the S.D. of {n -> 0.904794, a -> 1921.19, w -> 259.28} is
> 0.273892.
>
> I feel the answer is very close to the first one.
> I think Mathematica may change the parameters too quickly,so the
> caculation escape the local minimun of the first condition by only few
> steps.
>
> Q:Can I constraint Mathematica to change the fitting parameters
> slower? Don't escape the initial conditions I give too quickly.
> (Can Nonlinearmodelfit do this?)

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