Re: Weights in NonlinearRegress / NonlinearFit. Versus data errors

*To*: mathgroup at smc.vnet.net*Subject*: [mg85342] Re: Weights in NonlinearRegress / NonlinearFit. Versus data errors*From*: dh <dh at metrohm.ch>*Date*: Wed, 6 Feb 2008 06:37:51 -0500 (EST)*References*: <foc2nh$4o9$1@smc.vnet.net>

Hi Kris, if the errors are normal distributed and sigma is the standard deviation, then by minimizing the sum: Sum[ (e[i]/sigma[i])^2,{i}] you get a maximum likelihood estimate of your fit parameter. Your colleague seems to be right. hope this helps, Daniel Kristof Lebecki wrote: > Dear all, > > > > Introduction: it happens that we, physicists have to fit a given function > y(x) to a set of experimentally derived points {x_i,y_i}, i=1..n. I use for > that NonlinearRegress. > > > > It happenes, however, that the experimental points are known with different > accuracy. (We call usually such inaccuracy as an error.) Assume that we have > a vector of triples {x_i,y_i,dy_i}, i=1..n. Now, dy_i describes the > "y-error" of every point we want to fit. > > > > My first idea was to use Weights for that. Weights defined as: > > {w_i}= {1/dy_i} (the smaller the error the higher the weight). > > But my experienced colleague pointed out that what actually is here > minimized is: chi^2= \sum_i w_i*(e_i)^2. He prefers that sum to be > dimensionless, thus he argues that the weights should be defined as: > > {w_i}= {1/(dy_i)^2} > > > > And what is your opinion? > > > > > Regards, Kris > >