# Model and experiment fitting.

Robert Kern robert.kern at gmail.com
Fri Oct 20 17:14:45 CDT 2006

```Sebastian Żurek wrote:
> Hi!
>
> This is probably a silly question but I'm getting confused with a
> certain problem: a comparison between experimental data points (2D
> points set) and a model (2D points set - no analytical form).
>
> The physical model produces (by a sophisticated simulations done by an
> external program) some 2D points data and  one of my task is to compare
> those calculated data with an experimental one.
>
> The experimental and modeled data have form of 2D curves, build of n
> 2D-points, i.e.:
>
> expDat=[[x1,x2,x3,..xn],[y1,y2,y3,...,yn]]
> simDat=[[X1,X2,X3,...,Xn],[Y1,Y2,Y3,...,Yn]]
>
> The task of determining, let's say, a root mean squarred error (RMSe)
> is trivial if x1==X1, x2==X2, etc.
>
> In general, which is a common situation xk differs from Xk (k=0..n) and
> one may not simply compare succeeding Yk and yk (k=0..n) to determine
> the goodness-of-fit. The distance h=Xk-X(k-1) is constant, but similar
> distance m(k)=xk-x(k-1) depends on k-th point and is not a constant
> value, although the data array lengths for simulation and experiment are
> the same.

Your description is a bit vague. Do you mean that you have some model function f
that maps X values to Y values?

f(x) -> y

If that is the case, is there some reason that you cannot run your simulation
using the same X points as your experimental data?

OTOH, is there some other independent variable (say Z) that *is* common between

f(z) -> (x, y)

--
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless enigma
an underlying truth."
-- Umberto Eco

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