Hi, 2012/5/3 Gilles Sadowski <gil...@harfang.homelinux.org>: > Hello. > >> in this thread, >> http://mail-archives.apache.org/mod_mbox/commons-dev/201204.mbox/%3C20120418122114.GB32074%40dusk.harfang.homelinux.org%3E >> I suggested that we deprecate guessParametersErrors() and replace it >> with getParametersStandardDeviation(), since the implemented formula >> seems to be the accepted estimate for the sd of the optimized >> parameters. >> There was no reaction, but I don't think that meant agreement (!). > > There isn't even an agreement that this method should not be deleted... :-) > Indeed, people around here (working in astronomy) maintain that the error > they'd publish is the square-root of the diagonal element of the covariance > matrix. > > I've been busy coding a trivial example aimed at comparing the two formulae. > I'll probably attach the file to issue MATH-784 tomorrow. > >> Although I do think that guessParametersErrors() is a bit vague (if >> not confusing), I'm going to drop this proposal unless someone says he >> supports it. As far as I am concerned, MATH-784 would then be resolved >> (I stiil need to inquire about getSigma()). > > As hinted above, what we use here is > > for (int i = 0; i < covMat.length; i++) { > sigma[i] = FastMath.sqrt(covMat[i][i]); > } > > Thus, a > > double[] getSigma() { /* ... */ } > > method would be nice to have, IMO. > However, we should make quite clear in the Javadoc what is the meaning of > the returned "error" (in particular, as most users are no more statistician > than we are, there should probably be a simple explanation of when to use > which). > > > Best, > Gilles > > --------------------------------------------------------------------- > To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org > For additional commands, e-mail: dev-h...@commons.apache.org > this is interesting stuff. I can make the addition of the required getSigma() method. Only, I'm reluctant to call it getSigma(), as sigma would suggest a standard deviation, which in fact is returned by guessParametersErrors().
The only reference I was able to find where the diagonal elements are directly used is numerical recipes, and if I remember correctly, I think it was called $\Delta a$, and was derived from the $\chi-2$ distribution. So it basically returns a confidence interval, I think, while guessParametersErrors truly returns a standard deviation. Is that correct? In that case, we could call getSigma() just that: getConfidenceInterval (the associated probability might even be specified as a parameter, or decided once and for all in the javadoc). Is Gilles, the best thing to do would probably be a Monte-Carlo simulation, with several realizations of the same dataset. Then, you would have a distribution of the parameters, from which you would be able to compute the standard deviation. If you want, I can do that. Meanwhile, I've asked for the Bevington book, but inter-library loans can tae a while... Best regards, Sébastien --------------------------------------------------------------------- To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org For additional commands, e-mail: dev-h...@commons.apache.org
