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From koshino kazuhiro <kosh...@ri.ncvc.go.jp>
Subject Re: [math] Standard errors in estimated parameters using LevenbergMarquardtEstimator
Date Thu, 13 Dec 2007 01:58:38 GMT
Hello,

> Oooops. Sorry, my answer does not match your question. You asked about 
> parameters and I answered about observations (measurements).

The term "standard errors" in my sentences was ambiguity.
I should use covariance matrix rather than standard errors.

Your suggestion for RMS is very important because my measurements was 
degraded by statistical noises.

> So the proper answer is no, there is no way to get any information about 
> errors on parameters yet. One method to have an estimate of the quality 
> of the result is to check the eigenvalues related to the parameters. 
> Perhaps we could look at this after having included a Singular Value 
> Decomposition algorithm ? Is this what you want or do you have some 
> other idea ?

In LevenbergMarquardtEstimator.java (revision 560660),
a jacobian matrix is used to estimate parameters.
Using the jacobian matrix, could we obtain a covariance matrix, i.e. 
errors on parameters?
covariance matrix = (Jt * J)^(-1)
where J, Jt and ^(-1) denotes a jacobian, a transpose matrix of J and an 
inverse operator, respectively.

Kind Regards,

Koshino

> Luc
> 
>> the method (because it is your problems which defines both the model, the
>> parameters and the observations).
>> If you call it before calling estimate, it will use the initial values 
>> of the
>> parameters, if you call it after having called estimate, it will use the
>> adjusted values.
>>
>> Here is what the javadoc says about this method:
>>
>>    * Get the Root Mean Square value, i.e. the root of the arithmetic
>>    * mean of the square of all weighted residuals. This is related to the
>>    * criterion that is minimized by the estimator as follows: if
>>    * <em>c</em> is the criterion, and <em>n</em> is the number
of
>>    * measurements, then the RMS is <em>sqrt (c/n)</em>.
>>> I think that those values are very important to validate estimated
>>> parameters.
>>
>> It may sometimes be misleading. If your problem model is wrong and too
>> "flexible", and if your observation are bad (measurements errors), 
>> then you may
>> adjust too many parameters and have the bad model really follow the bad
>> measurements and give you artificially low residuals. Then you may think
>> everything is perfect which is false. This is about the same kind of 
>> problems
>> knowns as "Gibbs oscillations" for polynomial fitting when you use a 
>> too high
>> degree.
>>
>> Luc
>>
>>> Is use of classes in java.lang.reflect.* only way to get standard 
>>> errors?
>>>
>>> Kind Regards,
>>>
>>> Koshino
>>>
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>>
>>
>>
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> 
> 
> 
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> 


-- 
Kazuhiro Koshino, PhD
National Cardiovascular Center Research Institute
5-7-1Fujishirodai, Suita, Osaka 565-8565, JAPAN
Tel: +81-6-6833-5012 (ex.2559)
Fax: +81-6-6835-5429
E-mail:koshino@ri.ncvc.go.jp

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