[
https://issues.apache.org/jira/browse/MATH-176?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=12557998#action_12557998
]
Kazuhiro Koshino commented on MATH-176:
---------------------------------------
Sorry for late reply.
Degrees of freedom (dof) is defined by
n - p
, where n is a number of measurements, p is a number of parameters,
respectively.
However,
if n is equal to p, there is no freedom. It means that measurements determine
parameters uniquely and no need to validate the model (parameter problem).
If n < p, we cannot determine the parameters represent the measurements because
there are infinite number of parameter sets. For example, we want to represent
a measurement with y = ax + b,
where a and b are parameters, y is a measurement for an input x. There are
infinite straight lines passing through the point (x, y).
For your example of 2x = 3, n = 1 (a measurement = 3 for an input value of 2)
and p = 1 (parameter is x). Then the dof is 0.
If users will get errors in estimated parameters for the cases of n = p or n <
p, My idea is
1) AbstractEstimator throws EstimationException during calling
guessParametersErrors.
or
2) An additional method, which enables users to check the validity of the dof,
that is, n > p befor calling guessParametersErrors
My english is too poor. I hope that you will ask me any questions in my comment
patiently.
> Getting errors in estimated parameters using Estimator
> ------------------------------------------------------
>
> Key: MATH-176
> URL: https://issues.apache.org/jira/browse/MATH-176
> Project: Commons Math
> Issue Type: Improvement
> Affects Versions: 1.2
> Reporter: Kazuhiro Koshino
> Assignee: Luc Maisonobe
> Priority: Minor
> Fix For: 1.2
>
> Attachments: LevenbergMarquardtEstimator.java.diff
>
>
> To validate estimated parameters by GaussNewtonEstimator and
> LevenbergMarquardtEstimator, we need errors (or covariances) in the
> parameters.
--
This message is automatically generated by JIRA.
-
You can reply to this email to add a comment to the issue online.
