Least-Squares Fitting with asymetric errors

[Stewart V. Wright]

G'day Adam,

(Forwarding your personal reply back to the list...)

* Adam Kleczkowski <ak133@cam.ac.uk> [040505 17:38]:
> I'm probably picky, but this is not computational but statistical problem.
> Least-squares assumes that your errors are distributed according to a normal
> (Gaussian) distribution, which is symmetrical. Asymmetric errors require
> either a different definition of a likelihood or a transformation of data.

This is entirely true and entirely useless - like all good answers
from a Mathematician!  :-P

I am was somewhat aware of the subtleties of the problem, and that I'm
not exactly doing the Right Thing^TM.  However I thought that using
Least-Squares was a reasonable first step.

I must admit that I am at a bit of a loss of how to approach this
problem correctly (previously I have been known to take the square
root of the sum of the squares of the asymmetric errors as a 'good
enough at this precision' approach).

Can you suggest any alternative fitting methods for _non-linear_
functions to data that may, or may not have asymmetric error bars and
may, or may not be correlated?  Would you be able to suggest an
alternate definition of likelihood?


Cheers,

S.
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