TPSTest Class Reference

#include <TPSTest.h>

List of all members.

Public Member Functions
	TPSTest ()
	TPSTest (TH1 *h1, TH1 *h2)
	~TPSTest ()
TH1 *	GetFit (const char *fitName="newFitHist") const
double	GetInt (int histNum) const
double	GetLogLikelihood () const
int	GetNbins () const
int	GetNbinsX () const
int	GetNbinsY () const
int	GetNbinsZ () const
double	GetProb () const
double	GetRatio () const
int	GetStatus () const
int	SetHist (int histNum, TH1 *hist)
int	SetBinRangeX (int minBin, int maxBin)
int	SetBinRangeY (int minBin, int maxBin)
int	SetBinRangeZ (int minBin, int maxBin)
Private Member Functions
double	CalcContents (TH1 *hist, double scaleFactor)
void	CalcLogLikelihood ()
void	CalcProb ()
void	Initialize ()
int	SetStatus ()
Private Attributes
TH1 *	fFit
TH1 *	fH1
TH1 *	fH2
double	fH1Conts
double	fH2Conts
double	fH1Scale
double	fH2Scale
double	fLL
int	fMinBinX
int	fMaxBinX
int	fMinBinY
int	fMaxBinY
int	fMinBinZ
int	fMaxBinZ
int	fNbins
int	fNbinsX
int	fNbinsY
int	fNbinsZ
double	fProb
double	fRatio
int	fStatus
int	fZeroBins

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Detailed Description

TPSTest

"Point Significance Test"

Hypothesis test of the assumption that two TH1 objects were filled from the same probability distribution. A maximum likelihood method is used to find the most likely source PDF. The resulting probability is the confidence level of the hypothesis that the input TH1 objects are the result of Poisson distributed fluctuations about the maximum likelihood fit distribution.

Definition at line 21 of file TPSTest.h.

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Constructor & Destructor Documentation

TPSTest::TPSTest (   )

Definition at line 26 of file TPSTest.cxx. { // Default constructor fH1Conts = 0.; fH2Conts = 0.; fLL = -1.; fRatio = 0.; fStatus = -1 ; fMinBinX = 0 ; fMinBinY = 0 ; fMinBinZ = 0 ; fMaxBinX = 0 ; fMaxBinY = 0 ; fMaxBinZ = 0 ; fNbins = -1 ; fNbinsX = -1 ; fNbinsY = -1 ; fNbinsZ = -1 ; fZeroBins= -1 ; fFit = 0 ; fH1 = 0 ; fH2 = 0 ; }

TPSTest::TPSTest (  TH1 *  h1, TH1 *  h2 )

Definition at line 56 of file TPSTest.cxx. References fFit, fH1, fH1Conts, fH2, fH2Conts, fLL, fMaxBinX, fMaxBinY, fMaxBinZ, fMinBinX, fMinBinY, fMinBinZ, fNbins, fNbinsX, fNbinsY, fNbinsZ, fRatio, fStatus, fZeroBins, and Initialize(). { // Constructor with complete initialization (incl. error checking) fH1 = dynamic_cast<TH1*>(h1->Clone("fH1")); fH2 = dynamic_cast<TH1*>(h2->Clone("fH2")); fH1Conts = 0.; fH2Conts = 0.; fLL = -1.; fRatio = 0.; fStatus = -1 ; fMinBinX = 0 ; fMinBinY = 0 ; fMinBinZ = 0 ; fMaxBinX = 0 ; fMaxBinY = 0 ; fMaxBinZ = 0 ; fNbins = -1 ; fNbinsX = -1 ; fNbinsY = -1 ; fNbinsZ = -1 ; fZeroBins= -1 ; fFit = 0 ; Initialize(); }

TPSTest::~TPSTest (   )

Definition at line 88 of file TPSTest.cxx. References fFit, fH1, and fH2. { // Destructor if (fH1) delete fH1; fH1 = 0; if (fH2) delete fH2; fH2 = 0; if (fFit) delete fFit; fFit = 0; }

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Member Function Documentation

double TPSTest::CalcContents (  TH1 *  hist, double  scaleFactor )  [private]

Definition at line 299 of file TPSTest.cxx. Referenced by Initialize(). { // Calculate the number of entries contained within the min/max bounds // set for x,y,z (adjusted for scale factors applied to the histogram) // double hCont = 0.; for (int x = fMinBinX; x <= fMaxBinX; x++) for (int y = fMinBinY; y <= fMaxBinY; y++) for (int z = fMinBinZ; z <= fMaxBinZ; z++){ int bin = hist->GetBin(x,y,z); hCont += (x == 0 && y == 0 && z == 0)? 0. : hist->GetBinContent(bin)/scaleFactor; } return hCont; }

void TPSTest::CalcLogLikelihood (   )  [private]

Definition at line 316 of file TPSTest.cxx. References fFit, fH1, fH1Conts, fH2, fH2Conts, fLL, and fNbins. Referenced by Initialize(). { // Calculate logLikelihood of the provided histograms to the // best-fit distribution // fLL = 0.; fFit = dynamic_cast<TH1*>(fH1->Clone("FitHist")); fFit->SetBit(TH1::kCanRebin,false); fFit->Reset("ICE"); for (int x = fMinBinX; x <= fMaxBinX; x++) for (int y = fMinBinY; y <= fMaxBinY; y++) for (int z = fMinBinZ; z <= fMaxBinZ; z++){ int bin = fH1->GetBin(x,y,z); double h1i = fH1->GetBinContent(bin)/fH1Scale; double h2i = fH2->GetBinContent(bin)/fH2Scale; double fiti = (h1i+h2i)/(fH1Conts+fH2Conts); double fitiErr = TMath::Sqrt(h1i+h2i)/(fH1Conts+fH2Conts); fFit->SetBinContent(bin,fiti); fFit->SetBinError (bin,fitiErr); bool bUnderFlow = (bin==0); bool bOverFlow = (bin==fNbins+1); if (!bUnderFlow && !bOverFlow){ double fit1 = fH1Conts*fiti; double p1 = (h1i > 1.e2 || fit1 > 4.e2)? TMath::Gaus(h1i,fit1,TMath::Sqrt(fit1),true) : TMath::PoissonI(h1i,fit1); // protect PoissonI from crashing double LL1 = (p1 > 1.e-10)? TMath::Log(p1) : -1.e10; double fit2 = fH2Conts*fiti; double p2 = (h2i > 1.e2 || fit2 > 4.e2)? TMath::Gaus(h2i,fit2,TMath::Sqrt(fit2),true) : TMath::PoissonI(h2i,fit2); // protect PoissonI from crashing double LL2 = (p2 > 1.e-10)? TMath::Log(p2) : -1.e10; if (fiti > 1.e-20) fLL += LL1 + LL2; } // end if there are entries in >= one histogram && not u/overflow } // end (3D) for loop over bins return; }

void TPSTest::CalcProb (   )  [private]

Definition at line 364 of file TPSTest.cxx. References fFit, fH1, fH2, fNbins, fProb, and fZeroBins. Referenced by Initialize(). { // Calculate the confidence level of the fit assuming Poisson distributed // measurements (does NOT include u/overflow bins in the calculation). // fProb = 1.; fZeroBins = 0 ; double logQ = 0.; unsigned int nBins = 0 ; for (int x = fMinBinX; x <= fMaxBinX; x++) for (int y = fMinBinY; y <= fMaxBinY; y++) for (int z = fMinBinZ; z <= fMaxBinZ; z++){ int bin = fH1->GetBin(x,y,z); double h1i = fH1 ->GetBinContent(bin)/fH1Scale; double fit1 = fFit->GetBinContent(bin)*fH1Conts; double h2i = fH2 ->GetBinContent(bin)/fH2Scale; double fit2 = fFit->GetBinContent(bin)*fH2Conts; bool bUnderFlow = (bin==0); bool bOverFlow = (bin==fNbins+1); if (!bUnderFlow && !bOverFlow && fit1 > 0. && fit2 > 0. ){ nBins++; // Get total probability contained within // (fit1-|fit1-h1i|,fit1+|fit1-h1i|) double diff1 = TMath::Abs(fit1-h1i); int start1 = (fit1-diff1 > 0.)? TMath::CeilNint(fit1-diff1) : 0; int end1 = TMath::FloorNint(fit1+diff1); double prob1 = 0.; for (int i = start1; i <= end1; i++) { prob1 += (i > 1.e2 || fit1 > 4.e2)? TMath::Gaus(i,fit1,TMath::Sqrt(fit1),true) : TMath::PoissonI(i,fit1); // protect PoissonI from crashing } // Get total probability contained within // (fit2-|fit2-h2i|,fit2+|fit2-h2i|) double diff2 = TMath::Abs(fit2-h2i); int start2 = (fit2-diff2 > 0.)? TMath::CeilNint(fit2-diff2) : 0; int end2 = TMath::FloorNint(fit2+diff2); double prob2 = 0.; for (int i = start2; i <= end2; i++) { prob2 += (i > 1.e2 || fit2 > 4.e2)? TMath::Gaus(i,fit2,TMath::Sqrt(fit2),true) : TMath::PoissonI(i,fit2); // protect PoissonI from crashing } // Confidence Levels double binCL1 = (1.-prob1); // c.l. for histogram1 bin i double binCL2 = (1.-prob2); // c.l. for histogram2 bin i logQ += (binCL1 > 0.)? TMath::Log(binCL1) : 0.; logQ += (binCL2 > 0.)? TMath::Log(binCL2) : 0.; } // end if not u/overflow bin or zero entries bin if (!(fit1 > 0.) || !(fit2 > 0.)) fZeroBins++; } // end (3D) for loop over bins fProb = TMath::Prob(-2*logQ,2*2*nBins); return; }

TH1 * TPSTest::GetFit (  const char *  fitName = "newFitHist"  )  const

Definition at line 97 of file TPSTest.cxx. References fFit, and fStatus. { // Return a pointer to a clone of the pdf histogram best fit to the 2 input // histograms. Optional argument, fitName, will be the name of the new // histogram (default is "newFitHist"). The pdf fit histogram is normalized // to area 1. The corresponding fit to each input histogram then is // found by scaling the fit histogram to the number of entries in the input // histogram of interest. // if (fStatus != 0) return 0; return dynamic_cast<TH1*>(fFit->Clone(fitName)); }

double TPSTest::GetInt (  int  histNum  )  const

Definition at line 111 of file TPSTest.cxx. References fStatus. { // Returns the integral of the contents contained within the bounds set // by SetBinRangeX(), SetBinRangeY(), SetBinRangeZ() for histogram // 'histNum' (1 or 2). // if (histNum == 1 && fStatus == 0) return fH1Conts; else if (histNum == 2 && fStatus == 0) return fH2Conts; else return -1.; }

double TPSTest::GetLogLikelihood (   )  const

Definition at line 126 of file TPSTest.cxx. References fStatus. { // Returns the loglikelihood of the combined fit to the // "best-fit true" distribution // if (fStatus != 0) return -1.; return fLL; }

int TPSTest::GetNbins (   )  const

Definition at line 136 of file TPSTest.cxx. References fStatus. { // Total number of bins (not including u/overflow) // if (fStatus != 0) return -1; return fNbins; }

int TPSTest::GetNbinsX (   )  const

Definition at line 145 of file TPSTest.cxx. References fStatus. { // Number of X bins (not including u/overflow) // if (fStatus != 0) return -1; return fNbinsX; }

int TPSTest::GetNbinsY (   )  const

Definition at line 154 of file TPSTest.cxx. References fStatus. { // Number of Y bins (not including u/overflow) // if (fStatus != 0) return -1; return fNbinsY; }

int TPSTest::GetNbinsZ (   )  const

Definition at line 163 of file TPSTest.cxx. References fStatus. { // Number of Z bins (not including u/overflow) // if (fStatus != 0) return -1; return fNbinsZ; }

double TPSTest::GetProb (   )  const

Definition at line 172 of file TPSTest.cxx. References fStatus. { // // Returns the significance of the hypothesis that both histograms // were filled from the same ('unknown') probability distribution. We // assume that the maximum likelihood fit distribution is the source // PDF, providing the bin-by-bin mean value of the Poisson-distributed // measurement. The confidence level is then calculated as the total // probability that the product of bin-by-bin confidence levels is at // most what is observed. // // Total significance (c.l.) is the (N-1)-dimensional integral of // P = Integral[Q/prod[p_i,{i,0,N-1}],{p_i,0,1}] bounded by the // (N-1)-dimensional hypercube of total volume 1.0 (where Q is the // product of significance levels we wish to combine, and N is the // number of probabilities combined; for us, N = number of bins). The // general solution to this is: P = Q*Sum[((-LnQ)^k)/k!,{k,0,(N-1)}], // verified by eqn (2) of: W.A.Wallis, Econometrica 10, 229 (1942). // // The quantity -2Ln(Q) explicitly follows a chiSquared probability // distribution with 2*(# indiv. probabilities) degrees of freedom. // Note that this statistic is *exact* and NOT an asymptotic form. Also, // this test statistic is NOT explicitly related to the chi-squared // goodness-of-fit test! // // A word of warning: for very few entries per bin (< ~5), the returned // probability will be 'low' even for compatible input histograms. The // cause of this is the assumption that the individual significance // estimates for each point (bin) are continuous. This assumption is // OK if you have many bins with a number of entries inconsistent with // zero, otherwise the discreteness of the Poisson distribution invalidates // this assumption severely. To remedy this, one must tabulate all the // possible significance values per bin and enumerate every possible // product of them across the bins. It is beyond the scope of this // particular implementation to do so. // // This test is not sensitive to the sign of the fluctuations about the // mean, so may be combined with any of a variety of sign tests to // increase the power and effect of these tests. // // Overflow and Underflow bins are explicitly not included in the // calculation. // if (fStatus != 0) return 0.; return fProb; }

double TPSTest::GetRatio (   )  const

Definition at line 220 of file TPSTest.cxx. References fStatus. { // Ratio of areas of the input histograms (0. < ratio <= 1.) // if (fStatus != 0) return 0.; return fRatio; }

int TPSTest::GetStatus (   )  const

Definition at line 229 of file TPSTest.cxx. { // Status flag: // -1 = TPSTest is not initialized (add histograms with SetHist) // 0 = OK // 1 = One of the histograms does not exist // 2 = Different histogram types // 3 = Different number of bins // 4 = One of the histograms is empty // 5 = Invalid fit range // return fStatus; }

void TPSTest::Initialize (   )  [private]

Definition at line 435 of file TPSTest.cxx. References CalcContents(), CalcLogLikelihood(), CalcProb(), fFit, fH1, fH1Conts, fH1Scale, fH2, fH2Conts, fH2Scale, fLL, fMaxBinX, fMaxBinY, fMaxBinZ, fNbins, fNbinsX, fNbinsY, fNbinsZ, fRatio, fStatus, fZeroBins, and SetStatus(). Referenced by SetBinRangeX(), SetBinRangeY(), SetBinRangeZ(), SetHist(), and TPSTest(). { // Fills in data members; does all of the initialization(!). // fLL = -1.; fH1Conts = 0.; fH2Conts = 0.; fH1Scale = 1.; fH2Scale = 1.; fRatio = 0.; fNbins = -1 ; fNbinsX = -1 ; fNbinsY = -1 ; fNbinsZ = -1 ; fZeroBins= -1 ; fStatus = -1 ; if (fFit) delete fFit; fFit = 0; // are we OK to proceed? SetStatus(); if (fStatus == 0) { // do all the dirty work here . . . fNbinsX = fH1->GetNbinsX(); fNbinsY = 0; fNbinsZ = 0; fNbins = fNbinsX; // does NOT include under/overflow fZeroBins= 0; // will be adjusted by CalcProb(); if (fH1->GetDimension() > 1) { fNbinsY = fH1->GetNbinsY(); fNbins *= fNbinsY; } if (fH1->GetDimension() > 2) { fNbinsZ = fH1->GetNbinsZ(); fNbins *= fNbinsZ; } fH1Scale = (fH1->GetSumOfWeights() + fH1->GetBinContent(0) + fH1->GetBinContent(fNbins+1))/ fH1->GetEntries(); // accounts for a TH1::Scale() fH2Scale = (fH2->GetSumOfWeights() + fH2->GetBinContent(0) + fH2->GetBinContent(fNbins+1))/ fH2->GetEntries(); // accounts for a TH1::Scale() if (fMaxBinX == 0) fMaxBinX = fNbinsX; if (fMaxBinY == 0) fMaxBinY = fNbinsY; if (fMaxBinZ == 0) fMaxBinZ = fNbinsZ; fH1Conts = CalcContents(fH1,fH1Scale); fH2Conts = CalcContents(fH2,fH2Scale); fRatio = 0.; if (fH1Conts > 0 && fH2Conts > 0){ fRatio = (fH1Conts > fH2Conts)? fH2Conts/fH1Conts : fH1Conts/fH2Conts ; } CalcLogLikelihood(); CalcProb(); } // end if status is OK if (fFit) fFit->SetBit(TH1::kCanRebin, true); return; }

int TPSTest::SetBinRangeX (  int  minBin, int  maxBin )

Definition at line 244 of file TPSTest.cxx. References fMaxBinX, fMinBinX, and Initialize(). { // Change the bin range in the x-direction; return status // fMinBinX = minBin; fMaxBinX = maxBin; Initialize(); return fStatus; }

int TPSTest::SetBinRangeY (  int  minBin, int  maxBin )

Definition at line 257 of file TPSTest.cxx. References fMaxBinY, fMinBinY, and Initialize(). { // Change the bin range in the y-direction; return status // fMinBinY = minBin; fMaxBinY = maxBin; Initialize(); return fStatus; }

int TPSTest::SetBinRangeZ (  int  minBin, int  maxBin )

Definition at line 270 of file TPSTest.cxx. References fMaxBinZ, fMinBinZ, and Initialize(). { // Change the bin range in the z-direction; return status // fMinBinZ = minBin; fMaxBinZ = maxBin; Initialize(); return fStatus; }

int TPSTest::SetHist (  int  histNum, TH1 *  hist )

Definition at line 283 of file TPSTest.cxx. References fH1, fH2, and Initialize(). { // Change histograms; return status (histNum must be 1 or 2) // if (histNum == 1) fH1 = dynamic_cast<TH1*>(hist->Clone("fH1")); else if (histNum == 2) fH2 = dynamic_cast<TH1*>(hist->Clone("fH2")); else return fStatus; Initialize(); return fStatus; }

int TPSTest::SetStatus (   )  [private]

Definition at line 506 of file TPSTest.cxx. References fH1, fH2, fMaxBinX, fMaxBinY, fMaxBinZ, fMinBinX, fMinBinY, fMinBinZ, and fStatus. Referenced by Initialize(). { // Make sure our histograms are sufficient to proceed with calculation // writes detailed warnings to cout if there's a problem. // Status flag: // -1 = TPSTest is not initialized (add histograms with SetHist) // 0 = OK // 1 = One of the histograms does not exist // 2 = Different histogram types // 3 = Different number of bins // 4 = One of the histograms is empty // 5 = Invalid fit range // fStatus = -1; // not yet set // check for various error states that would prevent calculation if (!fH1 || !fH2) fStatus = 1; // >= 1 histogram does not exist else { TClass* cl1 = fH1->Class(); TClass* cl2 = fH2->Class(); if (!(cl1->InheritsFrom(cl2)) || !(cl2->InheritsFrom(cl1)) ) fStatus = 2; // different types of histogram else if ((fH1->GetNbinsX() != fH2->GetNbinsX()) || (fH1->GetDimension() > 1 && fH1->GetNbinsY() != fH2->GetNbinsY()) || (fH1->GetDimension() > 2 && fH1->GetNbinsZ() != fH2->GetNbinsZ()) ) fStatus = 3; // different number of bins in each histogram else if (fH1->GetEntries() <= 0. || fH2->GetEntries() <= 0. ) fStatus = 4; // one of the histograms is empty else if (fMaxBinX < fMinBinX || fMaxBinY < fMinBinY || fMaxBinZ < fMinBinZ || fMinBinX > fH1->GetNbinsX() || fMinBinX > fH2->GetNbinsX() || fMinBinY > fH1->GetNbinsY() || fMinBinY > fH2->GetNbinsY() || fMinBinZ > fH1->GetNbinsZ() || fMinBinZ > fH2->GetNbinsZ() || fMaxBinX < 0 || fMaxBinY < 0 || fMaxBinZ < 0 ) fStatus = 5; // histogram range is wrong else fStatus = 0; // we're A-OK } // end else: both histograms exist return fStatus; }

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Member Data Documentation

TH1* TPSTest::fFit [private]

Definition at line 53 of file TPSTest.h. Referenced by CalcLogLikelihood(), CalcProb(), GetFit(), Initialize(), TPSTest(), and ~TPSTest().

TH1* TPSTest::fH1 [private]

Definition at line 54 of file TPSTest.h. Referenced by CalcLogLikelihood(), CalcProb(), Initialize(), SetHist(), SetStatus(), TPSTest(), and ~TPSTest().

double TPSTest::fH1Conts [private]

Definition at line 56 of file TPSTest.h. Referenced by CalcLogLikelihood(), Initialize(), and TPSTest().

double TPSTest::fH1Scale [private]

Definition at line 58 of file TPSTest.h. Referenced by Initialize().

TH1* TPSTest::fH2 [private]

Definition at line 55 of file TPSTest.h. Referenced by CalcLogLikelihood(), CalcProb(), Initialize(), SetHist(), SetStatus(), TPSTest(), and ~TPSTest().

double TPSTest::fH2Conts [private]

Definition at line 57 of file TPSTest.h. Referenced by CalcLogLikelihood(), Initialize(), and TPSTest().

double TPSTest::fH2Scale [private]

Definition at line 59 of file TPSTest.h. Referenced by Initialize().

double TPSTest::fLL [private]

Definition at line 60 of file TPSTest.h. Referenced by CalcLogLikelihood(), Initialize(), and TPSTest().

int TPSTest::fMaxBinX [private]

Definition at line 62 of file TPSTest.h. Referenced by Initialize(), SetBinRangeX(), SetStatus(), and TPSTest().

int TPSTest::fMaxBinY [private]

Definition at line 64 of file TPSTest.h. Referenced by Initialize(), SetBinRangeY(), SetStatus(), and TPSTest().

int TPSTest::fMaxBinZ [private]

Definition at line 66 of file TPSTest.h. Referenced by Initialize(), SetBinRangeZ(), SetStatus(), and TPSTest().

int TPSTest::fMinBinX [private]

Definition at line 61 of file TPSTest.h. Referenced by SetBinRangeX(), SetStatus(), and TPSTest().

int TPSTest::fMinBinY [private]

Definition at line 63 of file TPSTest.h. Referenced by SetBinRangeY(), SetStatus(), and TPSTest().

int TPSTest::fMinBinZ [private]

Definition at line 65 of file TPSTest.h. Referenced by SetBinRangeZ(), SetStatus(), and TPSTest().

int TPSTest::fNbins [private]

Definition at line 67 of file TPSTest.h. Referenced by CalcLogLikelihood(), CalcProb(), Initialize(), and TPSTest().

int TPSTest::fNbinsX [private]

Definition at line 68 of file TPSTest.h. Referenced by Initialize(), and TPSTest().

int TPSTest::fNbinsY [private]

Definition at line 69 of file TPSTest.h. Referenced by Initialize(), and TPSTest().

int TPSTest::fNbinsZ [private]

Definition at line 70 of file TPSTest.h. Referenced by Initialize(), and TPSTest().

double TPSTest::fProb [private]

Definition at line 71 of file TPSTest.h. Referenced by CalcProb().

double TPSTest::fRatio [private]

Definition at line 72 of file TPSTest.h. Referenced by Initialize(), and TPSTest().

int TPSTest::fStatus [private]

Definition at line 73 of file TPSTest.h. Referenced by GetFit(), GetInt(), GetLogLikelihood(), GetNbins(), GetNbinsX(), GetNbinsY(), GetNbinsZ(), GetProb(), GetRatio(), Initialize(), SetStatus(), and TPSTest().

int TPSTest::fZeroBins [private]

Definition at line 74 of file TPSTest.h. Referenced by CalcProb(), Initialize(), and TPSTest().

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The documentation for this class was generated from the following files:

• TPSTest.h
• TPSTest.cxx

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