Re: NonlinearFit
- To: mathgroup at smc.vnet.net
- Subject: [mg19700] Re: NonlinearFit
- From: peter.buttgereit at pironet.de (Peter Buttgereit)
- Date: Sat, 11 Sep 1999 16:36:05 -0400
- Organization: communication works
- References: <7r24q2$6qd@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
[This followup was posted to comp.soft-sys.math.mathematica and a copy was sent to the cited author.] In article <7r24q2$6qd at smc.vnet.net>, virgil.stokes at neuro.ki.se says... > In reference to Statistics `NonlinearFit` (vers. 1.4, author: John M. Novak) > for Mathematica Version 3.0. > > I would like to be able to replace the minimization criterion > that is currently in this package (least-squares). I am trying to > find a different type of minimization criterion -- one that > performs better (hopefully) for my particular problem. > > Is it possible to use this package such that one can override the > current least-squares criterion with a user defined criterion? > > -- Virgil > > > Dear Virgil As like as William I would be curious about Your ideas other than least-squares optimisation... The L-M-Algorithm is essentially least-squares based -- there is no way to change this criterion. Also, using absolute distances (or whatever) will complicate confidence interval estimation considerably. If You are unhappy with least-squares I suppose You have noisy data or some problems with "outliers". In this case You can either "clean up" Your data in advance of fitting or use a suitable transformation. I.e. using least-squares fitting on the logarithms of Your data will minimize over the sum of squares of logarithms of the deviations -- noisiness and outlier problem are somewhat reduced if the data model allows for the transformation. Further, You can define Your own criterion this way: Fit "the model" using L-M (i.e.) Define a criterion to be minimised/maximised based on the residuals (sum, sum of squares, whatever suitable) and then use FindMinium[] to optimise over Your criterion. For me this method was a affordable solution occasionally ( must have been posted in this group some years ago). KR, Peter