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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

> 

> 




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