Re: integer model parameters

On Sun, Mar 04, 2012 at 17:21 -0500, David P. Huenemoerder wrote:
>
>     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).

Algorithms for integer optimization do exist, but isis doesn't
currently provide any.

The optimization methods in isis were not designed to provide
special treatment for integer-valued parameters.  You could set
step=1, but different optimizers use 'step' in different ways.
Some interpret it as an initial suggestion, some ignore it
altogether.

In principle, you can use a generic optimization method as you
have described, and simply map a continuous fit parameter onto
an integer, e.g. n = 2*nint(x)+1.

In practice, this may cause convergence problems because the
fit statistic will presumably make discontinous jumps whenever
the integer-valued fit parameter changes.

In that situation, optimizers that don't rely directly on
numerical derivative information might perform better --
e.g. simplex, diffevol might work better than mpfit.

Thanks,
-John
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