Re: Fitting Functions

From: Franz Heymann (notfranz.heymann_at_btopenworld.com)
Date: 06/16/04 

Date: Wed, 16 Jun 2004 22:42:48 +0000 (UTC)

"Gregory L. Hansen" <glhansen@steel.ucs.indiana.edu> wrote in message
news:capl9s$he4$1@hood.uits.indiana.edu...
> In article <sQOzc.31$45.13163@news.uchicago.edu>,
> <mmeron@cars3.uchicago.edu> wrote:
> >In article <cann9o$t4h$1@hood.uits.indiana.edu>,
> >glhansen@steel.ucs.indiana.edu (Gregory L. Hansen) writes:
> >>
> >>It seems so simple; let the computer fit y0+A*exp(-invtau*x) to a
peice of
> >>data and that's that. But depending on the starting conditions I
got
> >>invtau = 0.246, 0.405, 0.467, and they all looked pretty good.
And I fit
> >>to my own function, y0+A*exp(-invtau(x-x0)) with x0 held constant,
and got
> >>invtau=0.626. That looks a lot more like the value I expected, so
that's
> >>what I'll keep. What the hell, it's as good as any other. Lowest
> >>chisquare, but the chisquares of the first three only differed by
a few
> >>percent.
> >>
> >>When fitting to data like that, how can I have reasonable
confidence that
> >>my number is the one that corresponds to the real world?
> >>
> >In general, you cannot. A sufficient amount of beer will improve
the
> >confidence (ale is better than lager in this respect) and few shots
of
> >Jack Daniels may work even better, but the effect is transient.
> >
> >To the point, if your fitting procedure estimates only the fit
> >parameters, not their errors as well, then it is not good enough.
>
> I use Igor Pro, and that will give fits, uncertainties, chi-squares,
> covariance matrices, confidence intervals... I don't even know what
> confidence intervals are.
>
> But to give an example from yesterday, these are four different fits
to
> the same set of data. The first three were fit to
y0+A*exp(-invtau*x),
> the fourth to y+A*exp(-invtau*(x-x0)) with x0 given and fixed.
>
> invtau chi_square
> -------------- ----------
> 0.245 +- 5e-13 9.92e-14
> 0.403 +- 0.154 9.50e-14
> 0.467 +- 0.163 9.40e-14
> 0.626 +- 0.194 9.32e-14

Something is not right.
How come your chi_squares are so minute?

[snip]

Franz

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