Hi Gerco, Gerco Onderwater wrote: > > Hi Rooters, > > One of the things I noticed when I try to fit a TH1 using log(likelihood) > maximization, is that it is so terribly slow. When I looked into > H1FitLikelihood, I saw that for each iteration and each bin log(N!) is > calculated. In my particular case, that takes a lot of time, since I have > about 3000 bins, with contents varying from no counts to about 100000 > counts. In order to fit that, I need about 500 iteration. So I have a few > questions: > > 1) Is there a way to avoid recalculating sum(log(Ni!)) for each iteration > because it is supposed to be constant as long as the fitting range > doesn't change? Yes, I agree that it is stupid to recalculate this sum at each fit iteration. I have modified the code in my development version to bypass this step. Loglikelihood fit is now faster than the normal chisquare technique. Thanks for this suggestion that was really simple to implement. > > 2) Is there a reason to keep the sum(log(Ni!)) at all? Because it is > constant, it has no effect on the maximization process (at least it > shouldn't). One only needs the likelihood for the calculation of the > errors. see above > > 3) Can I convince root that it should use my own log(L) calculation > when fitting a TH1 (without going throught the pain of initializing a > TMinuit myself, and executing one of the prehistorical 6-letter > commands). Or would I have to rewrite the TH1-class in order to get that > done? in 2.22 not. I have introduced this possibility in the development version. If you specify the option "U", TH1::Fit will use your own fitting procedure. > > 4) Wouldn't Sterlings approximation for log(N!) be a good idea for larger > N? Or can't one calculate the likelihood using the fact that the > Poisson distribution can be approximated by a Gaussian for large N > (what the threshold N should be, needs to be discussed, but a value of > the order of 50 to 100 seems appropriate). This is not necessary any more following the change in 1. Rene Brun > > In spite of everything, still a happy user, > > -- Gerco > > Dr. C.J.G. Onderwater > Nuclear Physics Laboratory > 312 Loomis Laboratory of Physics > University of Illinois at Urbana-Champaign > 1110 West Green Street > Urbana, IL 61801-3080 > Phone : (217) 244-7363 > Fax : (217) 333-1215 > E-mail: onderwat@uiuc.edu
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