class TLimit


 TLimit

 Class to compute 95% CL limits

 adapted from the mclimit code from Tom Junk (CLs method)
 see http://root.cern.ch/root/doc/TomJunk.pdf
 see http://cern.ch/thomasj/searchlimits/ecl.html
 see: Tom Junk,NIM A434, p. 435-443, 1999

 see also the following interesting references:
  Alex Read, "Presentation of search results: the CLs technique"
  Journal of Physics G: Nucl. Part. Phys. 28 2693-2704 (2002).
  http://www.iop.org/EJ/abstract/0954-3899/28/10/313

 A nice article is also available in the CERN yellow report with the proceeding
 of the 2000 CERN workshop on confidence intervals.

  Alex Read, "Modified Frequentist Analysis of Search Results (The CLs Method)"
  CERN 2000-005 (30 May 2000)

 see note about: "Should I use TRolke, TFeldmanCousins, TLimit?"
  in the TRolke class description.

Function Members (Methods)

public:

	TLimit()
	TLimit(const TLimit&)
virtual	~TLimit()
static TClass*	Class()
static TConfidenceLevel*	ComputeLimit(TLimitDataSource* data, Int_t nmc = 50000, bool stat = false, TRandom* generator = 0)
static TConfidenceLevel*	ComputeLimit(Double_t s, Double_t b, Int_t d, Int_t nmc = 50000, bool stat = false, TRandom* generator = 0)
static TConfidenceLevel*	ComputeLimit(TH1* s, TH1* b, TH1* d, Int_t nmc = 50000, bool stat = false, TRandom* generator = 0)
static TConfidenceLevel*	ComputeLimit(Double_t s, Double_t b, Int_t d, TVectorD* se, TVectorD* be, TObjArray, Int_t nmc = 50000, bool stat = false, TRandom generator = 0)
static TConfidenceLevel*	ComputeLimit(TH1* s, TH1* b, TH1* d, TVectorD* se, TVectorD* be, TObjArray, Int_t nmc = 50000, bool stat = false, TRandom generator = 0)
virtual TClass*	IsA() const
TLimit&	operator=(const TLimit&)
virtual void	ShowMembers(TMemberInspector& insp, char* parent)
virtual void	Streamer(TBuffer& b)
void	StreamerNVirtual(TBuffer& b)

protected:

static bool	Fluctuate(TLimitDataSource* input, TLimitDataSource* output, bool init, TRandom*, bool stat = false)
static Double_t	LogLikelihood(Double_t s, Double_t b, Double_t b2, Double_t d)

Data Members

private:

static TOrdCollection*	fgSystNames	Collection of systematics names
static TArrayD*	fgTable	a log table... just to speed up calculation

Class Charts

Inheritance Inherited Members Includes Libraries

Function documentation

TConfidenceLevel * ComputeLimit(TLimitDataSource* data, Int_t nmc = 50000, bool stat = false, TRandom* generator = 0)

 class TLimit

 Algorithm to compute 95% C.L. limits using the Likelihood ratio
 semi-bayesian method.
 It takes signal, background and data histograms wrapped in a
 TLimitDataSource as input and runs a set of Monte Carlo experiments in
 order to compute the limits. If needed, inputs are fluctuated according
 to systematics. The output is a TConfidenceLevel.

 class TLimitDataSource


 Takes the signal, background and data histograms as well as different
 systematics sources to form the TLimit input.

  class TConfidenceLevel


 Final result of the TLimit algorithm. It is created just after the
 time-consuming part and can be stored in a TFile for further processing.
 It contains light methods to return CLs, CLb and other interesting
 quantities.

 The actual algorithm...
 From an input (TLimitDataSource) it produces an output TConfidenceLevel.
 For this, nmc Monte Carlo experiments are performed.
 As usual, the larger this number, the longer the compute time,
 but the better the result.

Supposing that there is a plotfile.root file containing 3 histograms (signal, background and data), you can imagine doing things like:

    TFile* infile=new TFile("plotfile.root","READ");
    infile->cd();
    TH1* sh=(TH1*)infile->Get("signal");
    TH1* bh=(TH1*)infile->Get("background");
    TH1* dh=(TH1*)infile->Get("data");
    TLimitDataSource* mydatasource = new TLimitDataSource(sh,bh,dh);
    TConfidenceLevel *myconfidence = TLimit::ComputeLimit(mydatasource,50000);
    cout << "  CLs    : " << myconfidence->CLs()  << endl;
    cout << "  CLsb   : " << myconfidence->CLsb() << endl;
    cout << "  CLb    : " << myconfidence->CLb()  << endl;
    cout << "< CLs >  : " << myconfidence->GetExpectedCLs_b()  << endl;
    cout << "< CLsb > : " << myconfidence->GetExpectedCLsb_b() << endl;
    cout << "< CLb >  : " << myconfidence->GetExpectedCLb_b()  << endl;
    delete myconfidence;
    delete mydatasource;
    infile->Close();

More informations can still be found on this page.

bool Fluctuate(TLimitDataSource* input, TLimitDataSource* output, bool init, TRandom* , bool stat = false)

 initialisation: create a sorted list of all the names of systematics

TConfidenceLevel * ComputeLimit(TH1* s, TH1* b, TH1* d, Int_t nmc, bool stat, TRandom * generator)

 Compute limit.

TConfidenceLevel * ComputeLimit(TH1* s, TH1* b, TH1* d, TVectorD* se, TVectorD* be, TObjArray* l, Int_t nmc, bool stat, TRandom * generator)

 Compute limit.

TConfidenceLevel * ComputeLimit(Double_t s, Double_t b, Int_t d, Int_t nmc, bool stat, TRandom * generator)

 Compute limit.

TConfidenceLevel * ComputeLimit(Double_t s, Double_t b, Int_t d, TVectorD* se, TVectorD* be, TObjArray* l, Int_t nmc, bool stat, TRandom * generator)

 Compute limit.

Double_t LogLikelihood(Double_t s, Double_t b, Double_t b2, Double_t d)

 Compute LogLikelihood (static function)

TLimit()

{}

virtual ~TLimit()

{}