Re: Help with parameter estimation

• To: mathgroup at smc.vnet.net
• Subject: [mg50088] Re: Help with parameter estimation
• Date: Sat, 14 Aug 2004 01:50:58 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```On 8/13/04 at 5:56 AM, aramtal at yahoo.fr (Abd) wrote:

>Hi all, i am trying to estimate the parameters a, b, c, d from a
>given model. Let's say, for the sake of argument ,that the
>probability density function of the model is f[a,b,c,d]. And I have
>a dataset A with n elements. I want to find the parameters a, b, c,
>d, such that the sum (K= sum f[a,b,c,d]-A[[i]]) is minimized. So I
>used the command

>Findminimum[K, {a,a0},{b,b0}, {c,c0},{d,d0}]. But it seems that I
>have an infinite loop somewhere, since the program runs for hours
>on a relatively fast machine, without producing anything. Could
>anyone give me a hint, as to how to solve this problem.

It isn't possible to be specific about solving your problem without details of the problem. Having said that, I will point out finding a minimum in muli-dimensional space is inherently a difficult problem. And the degree to which you will be sucessful depends stongly on the data set, the initial search parameters and specific method being used to find the minimum.

There are several things you can try. Rather than let FindMinimum select the method used to find a local method, you could specify the method. You could try changing the starting point. You could use StepMonitor and/or EvaluationMonitor to get information on where FindMinium is searching for the local minimum and progress being made.

If none of the above are helpful, try NMinimize instead. NMinimize has different methods available that might work better for your data set and function.
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