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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



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