Re: Minimisation Problem
- To: mathgroup at smc.vnet.net
- Subject: [mg40812] Re: Minimisation Problem
- From: Raibatak Das <rd54 at cornell.edu>
- Date: Sat, 19 Apr 2003 22:59:52 -0400 (EDT)
- References: <b7nr2a$81s$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
just wanted to add this line to my earlier reply. if you are feeling industrious enough to work out the expression for Derivative[0, 0, 1][AltChiSq][x, y, p] you may specify that as the Gradient option in the FindMinimum call. Mike Costa wrote: >Dear All, > >I have a little minimization problem. I'm essentially >trying to fit data points to a curve, which, in >particular, means minimising the chi-square function >in order to obtain the desired parameters. However, >the curve-fitting aspect is not important for now. The >main problem boils down to this: given f(x, p), the >theoretical function, with x being the simulated data >points and p being the parameter(s) of interest, and >y(x) being the actual obtained function value given >the simulated data set x, the usual chi-square method >of determining p consists of minimising the chi-square >function > > ChiSq = Sigma[(f(x,p) - y(x))^2/y(x)] > >where Sigma represents the sum over all the data >points(I realise that there are other definitions for >chi-square, but let's use this for now). The little >twist is this: I want instead to minimise the >ALTERNATIVE CHI-SQUARE > > AltChiSq = Sigma[2(f-y)+(2y+1)Log[2y+1/2f+1]] > >where again Sigma represents the sum over all the data >points. I want to minimise AltChiSq to get the >parameter p. > >In my situation, the theoretical function f only has >one parameter that needs to be estimated > > f(x,p) = p(0.4 + 3.8Exp[-|Cos[x]|^0.75]), > >p being a kind of normalising factor. I would like to >know if there are any intrinsic functions in >Mathematica that can directly minimise a function like >AltChiSQ above. I recognise that the usual methods for >minimising functions like FindMinimum and such will >not work here due to the number of terms that Sigma >sums over (among other reasons). Is there any other >way to use FindMinimum in order to handle the function >AltChiSq? Or maybe, is there some way to somehow >change the default chi-square function that >Linear/NonLinearFit uses in order to instead minimise >AltChiSq? If these strategies lead to nowhere, can >anyone give a general strategy of how to tackle this >minimisation problem in Mathematica? > >Any suggestions would be greatly appreciated. Thanks. > >__________________________________________________ >Do you Yahoo!? >The New Yahoo! Search - Faster. Easier. Bingo >http://search.yahoo.com > > > -- ------------------------------------------------------------------------ * /Raibatak Das / * Department of Chemistry and Chemical Biology, Cornell University. Ithaca, NY 14853. Ph : 1-607-255-6141 email : rd54 at cornell.edu <mailto:rd54 at cornell.edu>