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Thread Subject:
non-linear least squares _ MLE

Subject: non-linear least squares _ MLE

From: Aidy

Date: 19 Jul, 2011 05:34:09

Message: 1 of 3

hi all,

I am confused about the concept of maximum likelihood estimation (MLE) and non-linear least squares.

I am using lsnonlin in matlab what seems to me to be a straight forward non linear least squares estimation. However, the book I used to find the cost function (i.e. objective error function) for the non linear least square estimation referred to thefinal solution ofthe unknown parameters as the maximum likelihood solution and thus a MLE.But did not provide an explanation.

If anyone can share some light, I would be grateful.

cheers
aiden

Subject: non-linear least squares _ MLE

From: Aidy

Date: 19 Jul, 2011 14:54:10

Message: 2 of 3

can anyone suggest a possible explanation?

Subject: non-linear least squares _ MLE

From: Matt J

Date: 19 Jul, 2011 15:34:09

Message: 3 of 3

"Aidy" wrote in message <j0350h$j52$1@newscl01ah.mathworks.com>...
>
> I am using lsnonlin in matlab what seems to me to be a straight forward non linear least squares estimation. However, the book I used to find the cost function (i.e. objective error function) for the non linear least square estimation referred to thefinal solution ofthe unknown parameters as the maximum likelihood solution and thus a MLE.But did not provide an explanation.
================

The two aren't necessarily different. If you have Gaussian data with mean f(x) where x are unknown parameters and f() is a non-linear function, then writing down the negative of the loglikelihood will give you a non-linear least squares cost function.

Hence MLE=nonlinear least squares in that case.

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