Hello. > I'm obviously missing something in my litterature review. I did a new > MC simulation, with a much smaller number of observation points > (namely 3, to fit a straight line!!!). It turns out that the formula > you are advocating for is the best estimate of the standard deviation > of the parameters. Could you please explain why this fomula differs > from formulas (34) and (35) in > http://mathworld.wolfram.com/LeastSquaresFitting.html?
Independently of the explanation to be provided by Dimitri, I think that there are code design arguments in favour of deprecating (and later, deleting) the "guessParametersErrors" method, as follows. In the context of the "optimization.general" package, one assumes that a Jacobian matrix is available. From there, the code in "AbstractLeastSquares" computes the covariance matrix, from which one can readily extract the "sigma". This can be done without computing the chi-square! [While, as you have probably noticed, the "guessParametersErrors" will not behave nicely if you don't call "updateResidualsAndCost()" beforehand.] For the class to be self-consistent, the story can end here: Any additional utilities can lead to wrong expectations from different types of users (as we've demonstrated here). Indeed, confidence intervals refer to additional variables (as Dimitri wrote: "By how much can a parameter change before the normalized chi2 changes by <some number>?"). Being able to answer those questions also involves the correlations between the parameters (cf. the plot I've attached to MATH-784), whereas "guessParametersErrors" does not take them into account. > I hope I'm not bothering you too much. I really would like to > understand, so that we could write an accurate javadoc and possibly > rename the method appropriately. For clarity's sake (design-wise), I propose to remove the "guessParametersErrors" method, and add a "getSigma" (as syntactic sugar). If you want to dig further into the confidence interval issues in order to provide the related functionality (similar to, but not limited to, the current "guessParametersErrors"), I propose that that code be located in the "stat" package (where, by the way, some of the utilities might already exist!). What do you think? Best regards, Gilles --------------------------------------------------------------------- To unsubscribe, e-mail: dev-unsubscr...@commons.apache.org For additional commands, e-mail: dev-h...@commons.apache.org
