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
571Fujishirodai, Suita, Osaka 5658565, JAPAN
Tel: +81668335012 (ex.2559)
Fax: +81668355429
Email:koshino@ri.ncvc.go.jp

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