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https://issues.apache.org/jira/browse/MATH-784?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
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Sébastien Brisard updated MATH-784:
-----------------------------------
Attachment: SyntheticData.java
Attached is a Monte-Carlo simulation where 100000 realizations of the same
dataset are sampled. This leads to a series of 100,000 optimized values of the
parameters of the model. Then, the standard deviation of these parameters can
be estimated, and compared to the value returned by
{{guessParametersErrors()}}. The match is very good. However, the match with
the sqrt of the diagonal elements of the covariance matrix is also very good.
Thinking about it, it's not a big surprise, since the two estimates differ only
by a factor {{sqrt(n/(n-m))}}, where {{n}} is the number of observations, and
{{m}} the number of parameters (if the fit is good, the optimum value of chi2
is nearly equal to {{n}}).
Also shown by this program: the sqrt of the diag coeffs of the covariance
matrix provide the 68% confidence interval on the parameters.
What remains to be explored
* use smaller number of observables (then {{n/(n-m)}} should be significantly
greater than 1),
* use observations which are not distributed according to a gaussian law.
> Javadoc of AbstractLeastSquaresOptimizer.guessParametersErrors() is too vague
> -----------------------------------------------------------------------------
>
> Key: MATH-784
> URL: https://issues.apache.org/jira/browse/MATH-784
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 3.0
> Reporter: Sébastien Brisard
> Assignee: Sébastien Brisard
> Labels: javadoc, optimization
> Fix For: 3.1
>
> Attachments: SyntheticData.java
>
>
> This bug report follows a recent discussion available
> [here|http://mail-archives.apache.org/mod_mbox/commons-dev/201204.mbox/%3C20120418122114.GB32074%40dusk.harfang.homelinux.org%3E].
> It is now recognized that the values returned by {{guessParametersErrors()}}
> are in fact known as (asymptotic) standard errors. The javadoc should be made
> more explicit. Besides, the values returned by this method should be tested.
> The reference datasets from [NIST|http://www.itl.nist.gov/div898/strd/] are
> to be used.
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