[ https://issues.apache.org/jira/browse/MATH784?page=com.atlassian.jira.plugin.system.issuetabpanels:alltabpanel
]
Sébastien Brisard updated MATH784:

Attachment: SyntheticData.java
Attached is a MonteCarlo 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/(nm))}}, 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/(nm)}} 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: MATH784
> URL: https://issues.apache.org/jira/browse/MATH784
> 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 [herehttp://mailarchives.apache.org/mod_mbox/commonsdev/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 [NISThttp://www.itl.nist.gov/div898/strd/]
are to be used.

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