Re: [Gnuplot-info] Outputs of fit: details of how they're defined

[Dan H. <dan...@ph...>]

On Mon, 20 Nov 2017, Daniel Hatton via gnuplot-info wrote (among other
things):

> - As long as the prior probability density over parameter space,
> evaluated at the point (L,M) = (l,m), is non-zero, the leading-order
> Laplace's method approximation to the standard deviation of the
> posterior probability distribution for L, marginalized over M, is
> √(2/((∂⁲(χ⁲)/∂L⁲)ₗ¸ₘ-((∂⁲(χ⁲)/(∂L∂M))ₗ¸ₘ)⁲/(∂⁲(χ⁲)/∂M⁲)ₗ¸ₘ)).
> - As long as the prior probability density over parameter space,
> evaluated at the point (L,M) = (l,m), is non-zero, the leading-order
> Laplace's method approximation to the standard deviation of the
> posterior probability distribution for M, marginalized over L, is
> √(2/((∂⁲(χ⁲)/∂M⁲)ₗ¸ₘ-((∂⁲(χ⁲)/(∂L∂M))ₗ¸ₘ)⁲/(∂⁲(χ⁲)/∂L⁲)ₗ¸ₘ)).
...
> I have a sneaking suspicion that the person who wrote the phrase
> "asymptotic standard error", both in the Gnuplot manual and in the
> comments of file <src/fit.c>, in the Gnuplot source code tree, _has_
> seen those two statements or something very like them in a published
> source.  If that person is on this mailing list, it'd be great if
> s/he could provide a reference, please.

I don't know how the gnuplot-info web archive will handle threading
across a four-year gap, but I finally found a reference for those
things:

Tierney et al. (1989), _J. Am. Stat. Assoc._ *84*(407):710-716,
doi:10.1080/01621459.1989.10478824.