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Re: Least-Squares Fitting with asymetric errors
On Wed, May 05, 2004 at 06:47:29PM +0100, Stewart V. Wright wrote:
> G'day Adam,
>
> * 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
How about the following almost-useless answer ...
> 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?
Not sure what you mean by 'non-linear' in this context.
If the errors in your data are correlated, then I have no clue.
If they are non-corellated, then a least-squares-like algorithm
can still be created (assuming that you know what the distribution
is). (And assuming that the known distribution has a 'nice' expansion
in moments.) Like so: compute not just the squares, but also N higher
moments, cubes, etc. (watch out for overflows!!) Then, you then
minimize not the least-square, but the formula that describes your
distribution in moments.
You still have to write a pile of code to do this :0
--linas