extraction of likelhood value

From: Jan Conrad <Jan.Conrad_at_cern.ch>
Date: Thu, 12 Jul 2007 10:34:18 +0200

Dear Rooters,

 I am running the included macro. The goal is to extract the likelihood value (or log likelihood, doesn't matter).

If fitting using chi2, using:

TVirtualFitter *fitter = TVirtualFitter::Fitter(hWimp); Double_t amin,edm,errdef;
Int_t nvpar,nparx;
fitter->GetStats(amin,edm,errdef,nvpar,nparx); Double_t chi2 = hWimp->GetFunction("fitSignal")->GetChisquare(); printf("amin=%g, chi2=%g\n", amin, chi2);

I get:
 amin=51.689, chi2=51.689

 .. which makes sense.

If fitting using LL (log likelihood), I get:

> amin=502.46, chi2=857560

The obtained fit parameters are similar (though the likelihood fit did not catastrophical fail), I would have expected the chi2 to be similar to the one obtained in the first case. Furthermore in

http://root.cern.ch/root/roottalk/roottalk00/1963.html

Rene says that amin = -2 logL. Is that really true ?

I am using ROOT v5.10/00 on
Scientific Linux CERN SLC release 4.2 (Beryllium) Linux 2.6.9-22.0.1.EL.cern

cheers, thanks,
Jan

ToyLL(){

//////////////////////////////////////////////////////////
//
// Jan Conrad (Stockholm University), conrad_at_physto.se

//

//////////////////////////////////////////////////////////

 Int_t nBinsChi2 = 50;

// generate histogram with E-2 spectrum

TH1F* hWimp = new TH1F("wimp","wimp",nBinsChi2,1e4,1e6);

// Powerlaw (function 1)
TF1 *f1 = new TF1("f1","(x/1.e5)**(-2.0)",1e4.,1e6);

// Double exponential (function 2).
TF1 *f2 = new TF1("f2","TMath::Exp(-1.e-5*x)",1e4,1e6);

Double_t WimpSpec(Double_t *x, Double_t *par) {   return par[0]*TMath::Exp(par[1]*x[0]); }        

   hWimp->Reset();    

   for (Int_t iExp=0; iExp<1000000; iExp++) {

     double ws = f2->GetRandom();
     hWimp->Fill(ws);

   }    

   hWimp->Sumw2();

// check signal fitting
 TF1 *fitSignal = new TF1("fitSignal",WimpSpec,1e4.,1e6,2);

 fitSignal->SetNpx(500);
 fitSignal->SetLineWidth(4);
 fitSignal->SetLineColor(kMagenta);
 fitSignal->SetParameters(1.e4,-1.e-4);

 //TF1 *f2 = new
TF1("f2","TMath::Exp(-1.e-4*x)+.2*TMath::Exp(-1.e-5*x)",1e4,1e6);  //return par[0]*TMath::Exp(par[1]*x[0])+par[2]*TMath::Exp(par[3]*x[0]);  hWimp->Fit("fitSignal","L,V,I");

 TVirtualFitter *fitter = TVirtualFitter::Fitter(hWimp);  Double_t amin,edm,errdef;
 Int_t nvpar,nparx;
 fitter->GetStats(amin,edm,errdef,nvpar,nparx);  Double_t chi2 = hWimp->GetFunction("fitSignal")->GetChisquare();  printf("amin=%g, chi2=%g\n", amin, chi2); }

---

J. Conrad, Physics Department, Stockholm University, AlbaNova, SE-10691 Stockholm, Sweden, http://www.particle.kth.se/~conrad Received on Thu Jul 12 2007 - 10:34:25 CEST