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From Sébastien Brisard (JIRA) <j...@apache.org>
Subject [jira] [Updated] (MATH-784) Javadoc of AbstractLeastSquaresOptimizer.guessParametersErrors() is too vague
Date Fri, 04 May 2012 06:16:52 GMT

     [ https://issues.apache.org/jira/browse/MATH-784?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel
]

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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