numRecipes

Class FeldmanCousins

java.lang.Object

numRecipes.FeldmanCousins

public class FeldmanCousins
extends java.lang.Object

Implementation of the Feldman-Cousins method to calcylate the upper limit at a given C.L.

Unified Approach to the classical statistical analysis of small signals
Gary J. Feldman and Robert D. Cousins

Physical Review D 57 3873 (1998)

Field Summary

Fields

Modifier and Type	Field and Description
protected static double	bgSearchStep
protected static double	confidenceLevel confidence level of the flux interval
protected static double	epsilon off set to the BG if BG=0
static boolean	inclusive
protected static double	nBackgroundRelMax
protected static double	nBackgroundRelMin Relative Background uncertainties
protected static double	signalSearchRangeMax Range of searching the signal interval range decided by the Ferlman-Cousins
protected static double	signalSearchRangeMin Range of searching the signal interval range decided by the Ferlman-Cousins
protected static double	signalSearchStep step size of searching the signal interval range decided by the Ferlman-Cousins
protected static boolean	treatBGuncertainties

Constructor Summary

Constructors

Constructor and Description
FeldmanCousins()

Method Summary

Methods

Modifier and Type	Method and Description
static double	getAverageUpperLimit(double nBackground) Calculate average upper limit of signals for expected background of nBackground.
static double	getConfidenceLevel()
static double	getLeastSignalForDiscovery(double nBackground, double nSignificance) Calculate the lower signal numbers that would be discovered by a given confidence level (default: 90%) with significance of nSignificance sigma.
static double	getLowerLimit(double nBackground, long nObserved) Calculate lower limit of number of signals for a given observed number, nObserved, in expectation of nBackground and return the result.
static double	getMaxRangeOfSignalIntervalCalculation()
static double	getMinRangeOfSignalIntervalCalculation()
protected static double	getPDFwithUncertainBG(double nSignal, double nBackground, long nObserved)
protected static double	getSignalToMaximizeProbability(double nBackground, long nObserved)
static double	getStepSizeOfSignalIntervalCalculation()
static double	getUpperLimit(double nBackground, long nObserved) Calculate upper limit of number of signals for a given observed number, nObserved, in expectation of nBackground and return the result.
protected static boolean	isNobservedWithinConfidenceBelt(double nSignal, double nBackground, long nObserved) Tells whether the given number of observed events are within the confidence belt for the given signal and expected background.
static void	main(java.lang.String[] args) The simple main method - display the 90% C.L.
static double	probabilityOfNobserved(double nSignal, double nBackground, long nObserved) Return the confidence level that the given number of observed events for the given signal and expected background.
static void	setConfidenceLevel(double cl)
static void	setRangeOfSignalIntervalCalculation(double min, double max, double stepSize) Set the range of signals in calculating the signal interval - min < signal < max
static void	setRelativeBackgroundUncertainty(double minusBGerr, double plusBGerr) Set the bacgkround uncertainty.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

confidenceLevel

protected static double confidenceLevel

confidence level of the flux interval

signalSearchRangeMin

protected static double signalSearchRangeMin

Range of searching the signal interval range decided by the Ferlman-Cousins

signalSearchRangeMax

protected static double signalSearchRangeMax

Range of searching the signal interval range decided by the Ferlman-Cousins

signalSearchStep

protected static double signalSearchStep

step size of searching the signal interval range decided by the Ferlman-Cousins

bgSearchStep

protected static double bgSearchStep

epsilon

protected static double epsilon

off set to the BG if BG=0

nBackgroundRelMin

protected static double nBackgroundRelMin

Relative Background uncertainties

nBackgroundRelMax

protected static double nBackgroundRelMax

treatBGuncertainties

protected static boolean treatBGuncertainties

inclusive

public static boolean inclusive

Constructor Detail

FeldmanCousins

public FeldmanCousins()

Method Detail

setRangeOfSignalIntervalCalculation

public static void setRangeOfSignalIntervalCalculation(double min,
                                       double max,
                                       double stepSize)

Set the range of signals in calculating the signal interval - min < signal < max

getMaxRangeOfSignalIntervalCalculation

public static double getMaxRangeOfSignalIntervalCalculation()

getMinRangeOfSignalIntervalCalculation

public static double getMinRangeOfSignalIntervalCalculation()

getStepSizeOfSignalIntervalCalculation

public static double getStepSizeOfSignalIntervalCalculation()

setConfidenceLevel

public static void setConfidenceLevel(double cl)

getConfidenceLevel

public static double getConfidenceLevel()

setRelativeBackgroundUncertainty

public static void setRelativeBackgroundUncertainty(double minusBGerr,
                                    double plusBGerr)

Set the bacgkround uncertainty. If you do not call this method, then the confidence belt calculation is performed assuming that background is KNOWN i.e, the exact Felman-Cousins recipe.

        double minusBGerr :  (BGminimum - BGmean)/BGmean
        double plusBGerr :   (BGmaximum - BGmean)/BGmean
        

isNobservedWithinConfidenceBelt

protected static boolean isNobservedWithinConfidenceBelt(double nSignal,
                                      double nBackground,
                                      long nObserved)

Tells whether the given number of observed events are within the confidence belt for the given signal and expected background. Determined by the FelmanCousins method based upon the likelihood ratio.

probabilityOfNobserved

public static double probabilityOfNobserved(double nSignal,
                            double nBackground,
                            long nObserved)

Return the confidence level that the given number of observed events for the given signal and expected background. Determined by the FelmanCousins method based upon the likelihood ratio.

getPDFwithUncertainBG

protected static double getPDFwithUncertainBG(double nSignal,
                           double nBackground,
                           long nObserved)

getSignalToMaximizeProbability

protected static double getSignalToMaximizeProbability(double nBackground,
                                    long nObserved)

getUpperLimit

public static double getUpperLimit(double nBackground,
                   long nObserved)

Calculate upper limit of number of signals for a given observed number, nObserved, in expectation of nBackground and return the result. The calculation is performed by the Feilman-Cousins method.

getLowerLimit

public static double getLowerLimit(double nBackground,
                   long nObserved)

Calculate lower limit of number of signals for a given observed number, nObserved, in expectation of nBackground and return the result. The calculation is performed by the Feilman-Cousins method.

getAverageUpperLimit

public static double getAverageUpperLimit(double nBackground)

Calculate average upper limit of signals for expected background of nBackground. It integrates getUpperLimit(nBackground,nobserved) convoluted with Poisson(nObserved), following the recipe in the Gary and Catherrin's paper.

getLeastSignalForDiscovery

public static double getLeastSignalForDiscovery(double nBackground,
                                double nSignificance)

Calculate the lower signal numbers that would be discovered by a given confidence level (default: 90%) with significance of nSignificance sigma. This evaluation is based on the signal discovery potential technique.

main

public static void main(java.lang.String[] args)
                 throws java.io.IOException

The simple main method - display the 90% C.L. interval for the Poisson signal mean.

Throws:

java.io.IOException