Re: integer model parameters

    Daniel> Off hand it seem to me that "fitting an integer-valued parameter"
    Daniel> is kind of an oxymoron   ;-)

Well, it's an analytical functional approximation for a line profile,
with enough dials to please nearly anyone. I don't a priori know
whether the exponent is to be frozen, or to be fit. (The model is
definitely degenerate if everything is left free).

The easy use is simulation, where I can pick whatever valid parameters
I want.  The inverse---fitting---is where some constraints must be
defined.   It just doesn't seem right to have a model parameter which
shouldn't be able to be left free, but if left free, can become
invalid and produce NaNs.

    Daniel> It would seem instead that you'd do the fit with your n fixed
    Daniel> in turn at, say,  2, 3, 4, 5, 6 and compare the restults for
    Daniel> these 'different' models.

Sure, but if I could do it manually, why can't I do it automatically?
If chisqr is better for n=3, then fitting should find it (within
limitations of searching multi-dimensional bumpy chi-squared spaces).

(Though a discrete or discontinuous variable probably borders on the
pathological and can't be trusted like other well behaved functions.)

    Daniel> Or, is there no way to define your model so that
    Daniel> non-integer values give reasonable/continuous/intermediate
    Daniel> results ?  replace a^n with sign(a)*abs(a)^n ?

No - that doesn't work.

I just consulted with my theorist collaborator who came up with the
formula, and the exponent is positive and odd (and maybe also zero;
another constraint - now n = 2*j+1 for j = 0, 1, 2..., or n=0).

It might be best left frozen, but it would be nice if the fit function
and optimizer could be given a reasonable clue.

-- Dave

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