//_________________________________________________
void TestJeffreysGaussSigma(){
// this one is VERY sensitive
// if the Gaussian is narrow ~ range(x)/nbins(x) then the peak isn't resolved
// and you get really bizzare shapes
// if the Gaussian is too wide range(x) ~ sigma then PDF gets renormalized
// and the PDF falls off too fast at high sigma
RooWorkspace w("w");
w.factory("Gaussian::g(x[0,-20,20],mu[0,-5,5],sigma[1,1,5])");
w.factory("n[100,.1,2000]");
w.factory("ExtendPdf::p(g,n)");
// w.var("sigma")->setConstant();
w.var("mu")->setConstant();
w.var("n")->setConstant();
w.var("x")->setBins(301);
RooDataHist* asimov = w.pdf("p")->generateBinned(*w.var("x"),ExpectedData());
RooFitResult* res = w.pdf("p")->fitTo(*asimov,Save(),SumW2Error(kTRUE));
asimov->Print();
res->Print();
TMatrixDSym cov = res->covarianceMatrix();
cout << "variance = " << (cov.Determinant()) << endl;
cout << "stdev = " << sqrt(cov.Determinant()) << endl;
cov.Invert();
cout << "jeffreys = " << sqrt(cov.Determinant()) << endl;
// w.defineSet("poi","mu,sigma");
//w.defineSet("poi","mu,sigma,n");
w.defineSet("poi","sigma");
w.defineSet("obs","x");
RooJeffreysPrior pi("jeffreys","jeffreys",*w.pdf("p"),*w.set("poi"),*w.set("obs"));
// pi.specialIntegratorConfig(kTRUE)->method1D().setLabel("RooAdaptiveGaussKronrodIntegrator1D") ;
pi.specialIntegratorConfig(kTRUE)->getConfigSection("RooIntegrator1D").setRealValue("maxSteps",3);
const RooArgSet* temp = w.set("poi");
pi.getParameters(*temp)->Print();
// return;
// return;
RooGenericPdf* test = new RooGenericPdf("test","test","sqrt(2.)/sigma",*w.set("poi"));
TCanvas* c1 = new TCanvas;
RooPlot* plot = w.var("sigma")->frame();
pi.plotOn(plot);
test->plotOn(plot,LineColor(kRed),LineStyle(kDotted));
plot->Draw();
}
void JeffreysPriorDemo(){
RooWorkspace w("w");
w.factory("Uniform::u(x[0,1])");
w.factory("mu[100,1,200]");
w.factory("ExtendPdf::p(u,mu)");
// w.factory("Poisson::pois(n[0,inf],mu)");
RooDataHist* asimov = w.pdf("p")->generateBinned(*w.var("x"),ExpectedData());
// RooDataHist* asimov2 = w.pdf("pois")->generateBinned(*w.var("n"),ExpectedData());
RooFitResult* res = w.pdf("p")->fitTo(*asimov,Save(),SumW2Error(kTRUE));
asimov->Print();
res->Print();
TMatrixDSym cov = res->covarianceMatrix();
cout << "variance = " << (cov.Determinant()) << endl;
cout << "stdev = " << sqrt(cov.Determinant()) << endl;
cov.Invert();
cout << "jeffreys = " << sqrt(cov.Determinant()) << endl;
w.defineSet("poi","mu");
w.defineSet("obs","x");
// w.defineSet("obs2","n");
RooJeffreysPrior pi("jeffreys","jeffreys",*w.pdf("p"),*w.set("poi"),*w.set("obs"));
// pi.specialIntegratorConfig(kTRUE)->method1D().setLabel("RooAdaptiveGaussKronrodIntegrator1D") ;
// pi.specialIntegratorConfig(kTRUE)->getConfigSection("RooIntegrator1D").setRealValue("maxSteps",10);
// JeffreysPrior pi2("jeffreys2","jeffreys",*w.pdf("pois"),*w.set("poi"),*w.set("obs2"));
// return;
RooGenericPdf* test = new RooGenericPdf("test","test","1./sqrt(mu)",*w.set("poi"));
TCanvas* c1 = new TCanvas;
RooPlot* plot = w.var("mu")->frame();
// pi.plotOn(plot, Normalization(1,RooAbsReal::Raw),Precision(.1));
pi.plotOn(plot);
// pi2.plotOn(plot,LineColor(kGreen),LineStyle(kDotted));
test->plotOn(plot,LineColor(kRed));
plot->Draw();
}
//_________________________________________________
void TestJeffreysGaussMean(){
RooWorkspace w("w");
w.factory("Gaussian::g(x[0,-20,20],mu[0,-5,5],sigma[1,0,10])");
w.factory("n[10,.1,200]");
w.factory("ExtendPdf::p(g,n)");
w.var("sigma")->setConstant();
w.var("n")->setConstant();
RooDataHist* asimov = w.pdf("p")->generateBinned(*w.var("x"),ExpectedData());
RooFitResult* res = w.pdf("p")->fitTo(*asimov,Save(),SumW2Error(kTRUE));
asimov->Print();
res->Print();
TMatrixDSym cov = res->covarianceMatrix();
cout << "variance = " << (cov.Determinant()) << endl;
cout << "stdev = " << sqrt(cov.Determinant()) << endl;
cov.Invert();
cout << "jeffreys = " << sqrt(cov.Determinant()) << endl;
// w.defineSet("poi","mu,sigma");
w.defineSet("poi","mu");
w.defineSet("obs","x");
RooJeffreysPrior pi("jeffreys","jeffreys",*w.pdf("p"),*w.set("poi"),*w.set("obs"));
// pi.specialIntegratorConfig(kTRUE)->method1D().setLabel("RooAdaptiveGaussKronrodIntegrator1D") ;
// pi.specialIntegratorConfig(kTRUE)->getConfigSection("RooIntegrator1D").setRealValue("maxSteps",3);
const RooArgSet* temp = w.set("poi");
pi.getParameters(*temp)->Print();
// return;
RooGenericPdf* test = new RooGenericPdf("test","test","1",*w.set("poi"));
TCanvas* c1 = new TCanvas;
RooPlot* plot = w.var("mu")->frame();
pi.plotOn(plot);
test->plotOn(plot,LineColor(kRed),LineStyle(kDotted));
plot->Draw();
}
double operator() (double *x, double *p) {
// 4 parameters
int dim = X.GetNrows();
int k = 0;
for (int i = 0; i<dim; ++i) { X[i] = x[i] - p[k]; k++; }
for (int i = 0; i<dim; ++i) {
CovMat(i,i) = p[k]*p[k];
k++;
}
for (int i = 0; i<dim; ++i) {
for (int j = i+1; j<dim; ++j) {
// p now are the correlations N(N-1)/2
CovMat(i,j) = p[k]*sqrt(CovMat(i,i)*CovMat(j,j));
CovMat(j,i) = CovMat(i,j);
k++;
}
}
if (debug) {
X.Print();
CovMat.Print();
}
double det = CovMat.Determinant();
if (det <= 0) {
Fatal("GausND","Determinant is <= 0 det = %f",det);
CovMat.Print();
return 0;
}
double norm = std::pow( 2. * TMath::Pi(), dim/2) * sqrt(det);
// compute the gaussians
CovMat.Invert();
double fval = std::exp( - 0.5 * CovMat.Similarity(X) )/ norm;
if (debug) {
std::cout << "det " << det << std::endl;
std::cout << "norm " << norm << std::endl;
std::cout << "fval " << fval << std::endl;
}
return fval;
}
