This class calculates the Kelvin functions Ber(x), Bei(x), Ker(x), Kei(x), and their first derivatives. -
- -End_Html */ +*/ //////////////////////////////////////////////////////////////////////////////// -/// Begin_Latex -/// Ber(x) = Ber_{0}(x) = Re#left[J_{0}#left(x e^{3#pii/4}#right)#right] -/// End_Latex -/// where x is real, and Begin_Latex J_{0}(z) End_Latex is the zeroth-order Bessel +/// \f[ +/// Ber(x) = Ber_{0}(x) = Re\left[J_{0}\left(x e^{3\pi i/4}\right)\right] +/// \f] +/// where x is real, and \f$J_{0}(z)\f$ is the zeroth-order Bessel /// function of the first kind. /// /// If x < fgMin (=20), Ber(x) is computed according to its polynomial /// approximation -/// Begin_Latex -/// Ber(x) = 1 + #sum_{n #geq 1}#frac{(-1)^{n}(x/2)^{4n}}{[(2n)!]^{2}} -/// End_Latex +/// \f[ +/// Ber(x) = 1 + \sum_{n \geq 1}\frac{(-1)^{n}(x/2)^{4n}}{[(2n)!]^{2}} +/// \f] /// For x > fgMin, Ber(x) is computed according to its asymptotic /// expansion: -/// Begin_Latex -/// Ber(x) = #frac{e^{x/#sqrt{2}}}{#sqrt{2#pix}} [F1(x) cos#alpha + G1(x) sin#alpha] - #frac{1}{#pi}Kei(x) -/// End_Latex -/// where Begin_Latex #alpha = #frac{x}{#sqrt{2}} - #frac{#pi}{8} End_Latex. -/// See also F1(x) and G1(x). +/// \f[ +/// Ber(x) = \frac{e^{x/\sqrt{2}}}{\sqrt{2\pi x}} [F1(x) cos\alpha + G1(x) sin\alpha] - \frac{1}{\pi}Kei(x) +/// \f] +/// where \f$\alpha = \frac{x}{\sqrt{2}} - \frac{\pi}{8}\f$. +/// +/// See also F1() and G1(). /// /// Begin_Macro /// { @@ -102,24 +100,25 @@ } //////////////////////////////////////////////////////////////////////////////// -/// Begin_Latex -/// Bei(x) = Bei_{0}(x) = Im#left[J_{0}#left(x e^{3#pii/4}#right)#right] -/// End_Latex -/// where x is real, and Begin_Latex J_{0}(z) End_Latex is the zeroth-order Bessel +/// \f[ +/// Bei(x) = Bei_{0}(x) = Im\left[J_{0}\left(x e^{3\pi i/4}\right)\right] +/// \f] +/// where x is real, and \f$J_{0}(z)\f$ is the zeroth-order Bessel /// function of the first kind. /// /// If x < fgMin (=20), Bei(x) is computed according to its polynomial /// approximation -/// Begin_Latex -/// Bei(x) = #sum_{n #geq 0}#frac{(-1)^{n}(x/2)^{4n+2}}{[(2n+1)!]^{2}} -/// End_Latex +/// \f[ +/// Bei(x) = \sum_{n \geq 0}\frac{(-1)^{n}(x/2)^{4n+2}}{[(2n+1)!]^{2}} +/// \f] /// For x > fgMin, Bei(x) is computed according to its asymptotic /// expansion: -/// Begin_Latex -/// Bei(x) = #frac{e^{x/#sqrt{2}}}{#sqrt{2#pix}} [F1(x) sin#alpha + G1(x) cos#alpha] - #frac{1}{#pi}Ker(x) -/// End_Latex -/// where Begin_Latex #alpha = #frac{x}{#sqrt{2}} - #frac{#pi}{8} End_Latex -/// See also F1(x) and G1(x). +/// \f[ +/// Bei(x) = \frac{e^{x/\sqrt{2}}}{\sqrt{2\pi x}} [F1(x) sin\alpha + G1(x) cos\alpha] - \frac{1}{\pi}Ker(x) +/// \f] +/// where \f$\alpha = \frac{x}{\sqrt{2}} - \frac{\pi}{8}\f$. +/// +/// See also F1() and G1(). /// /// Begin_Macro /// { @@ -161,29 +160,30 @@ //////////////////////////////////////////////////////////////////////////////// -/// Begin_Latex -/// Ker(x) = Ker_{0}(x) = Re#left[K_{0}#left(x e^{3#pii/4}#right)#right] -/// End_Latex -/// where x is real, and Begin_Latex K_{0}(z) End_Latex is the zeroth-order modified +/// \f[ +/// Ker(x) = Ker_{0}(x) = Re\left[K_{0}\left(x e^{3\pi i/4}\right)\right] +/// \f] +/// where x is real, and \f$K_{0}(z)\f$ is the zeroth-order modified /// Bessel function of the second kind. /// /// If x < fgMin (=20), Ker(x) is computed according to its polynomial /// approximation -/// Begin_Latex -/// Ker(x) = -#left(ln #frac{|x|}{2} + #gamma#right) Ber(x) + #left(#frac{#pi}{4} - #delta#right) Bei(x) + #sum_{n #geq 0} #frac{(-1)^{n}}{[(2n)!]^{2}} H_{2n} #left(#frac{x}{2}#right)^{4n} -/// End_Latex -/// where Begin_Latex #gamma = 0.577215664... End_Latex is the Euler-Mascheroni constant, -/// Begin_Latex #delta = #pi End_Latex for x < 0 and is otherwise zero, and -/// Begin_Latex -/// H_{n} = #sum_{k = 1}^{n} #frac{1}{k} -/// End_Latex +/// \f[ +/// Ker(x) = -\left(ln \frac{|x|}{2} + \gamma\right) Ber(x) + \left(\frac{\pi}{4} - \delta\right) Bei(x) + \sum_{n \geq 0} \frac{(-1)^{n}}{[(2n)!]^{2}} H_{2n} \left(\frac{x}{2}\right)^{4n} +/// \f] +/// where \f$\gamma = 0.577215664...\f$ is the Euler-Mascheroni constant, +/// \f$\delta = \pi\f$ for x < 0 and is otherwise zero, and +/// \f[ +/// H_{n} = \sum_{k = 1}^{n} \frac{1}{k} +/// \f] /// For x > fgMin, Ker(x) is computed according to its asymptotic /// expansion: -/// Begin_Latex -/// Ker(x) = #sqrt{#frac{#pi}{2x}} e^{-x/#sqrt{2}} [F2(x) cos#beta + G2(x) sin#beta] -/// End_Latex -/// where Begin_Latex #beta = #frac{x}{#sqrt{2}} + #frac{#pi}{8} End_Latex -/// See also F2(x) and G2(x). +/// \f[ +/// Ker(x) = \sqrt{\frac{\pi}{2x}} e^{-x/\sqrt{2}} [F2(x) cos\beta + G2(x) sin\beta] +/// \f] +/// where \f$\beta = \frac{x}{\sqrt{2}} + \frac{\pi}{8}\f$. +/// +/// See also F2() and G2(). /// /// Begin_Macro /// { @@ -227,29 +227,30 @@ //////////////////////////////////////////////////////////////////////////////// -/// Begin_Latex -/// Kei(x) = Kei_{0}(x) = Im#left[K_{0}#left(x e^{3#pii/4}#right)#right] -/// End_Latex -/// where x is real, and Begin_Latex K_{0}(z) End_Latex is the zeroth-order modified +/// \f[ +/// Kei(x) = Kei_{0}(x) = Im\left[K_{0}\left(x e^{3\pi i/4}\right)\right] +/// \f] +/// where x is real, and \f$K_{0}(z)\f$ is the zeroth-order modified /// Bessel function of the second kind. /// /// If x < fgMin (=20), Kei(x) is computed according to its polynomial /// approximation -/// Begin_Latex -/// Kei(x) = -#left(ln #frac{x}{2} + #gamma#right) Bei(x) - #left(#frac{#pi}{4} - #delta#right) Ber(x) + #sum_{n #geq 0} #frac{(-1)^{n}}{[(2n)!]^{2}} H_{2n} #left(#frac{x}{2}#right)^{4n+2} -/// End_Latex -/// where Begin_Latex #gamma = 0.577215664... End_Latex is the Euler-Mascheroni constant, -/// Begin_Latex #delta = #pi End_Latex for x < 0 and is otherwise zero, and -/// Begin_Latex -/// H_{n} = #sum_{k = 1}^{n} #frac{1}{k} -/// End_Latex +/// \f[ +/// Kei(x) = -\left(ln \frac{x}{2} + \gamma\right) Bei(x) - \left(\frac{\pi}{4} - \delta\right) Ber(x) + \sum_{n \geq 0} \frac{(-1)^{n}}{[(2n)!]^{2}} H_{2n} \left(\frac{x}{2}\right)^{4n+2} +/// \f] +/// where \f$\gamma = 0.577215664...\f$ is the Euler-Mascheroni constant, +/// \f$\delta = \pi\f$ for x < 0 and is otherwise zero, and +/// \f[ +/// H_{n} = \sum_{k = 1}^{n} \frac{1}{k} +/// \f] /// For x > fgMin, Kei(x) is computed according to its asymptotic /// expansion: -/// Begin_Latex -/// Kei(x) = - #sqrt{#frac{#pi}{2x}} e^{-x/#sqrt{2}} [F2(x) sin#beta + G2(x) cos#beta] -/// End_Latex -/// where Begin_Latex #beta = #frac{x}{#sqrt{2}} + #frac{#pi}{8} End_Latex -/// See also F2(x) and G2(x). +/// \f[ +/// Kei(x) = - \sqrt{\frac{\pi}{2x}} e^{-x/\sqrt{2}} [F2(x) sin\beta + G2(x) cos\beta] +/// \f] +/// where \f$\beta = \frac{x}{\sqrt{2}} + \frac{\pi}{8}\f$. +/// +/// See also F2() and G2(). /// /// Begin_Macro /// { @@ -298,10 +299,10 @@ /// If x < fgMin (=20), DBer(x) is computed according to the derivative of /// the polynomial approximation of Ber(x). Otherwise it is computed /// according to its asymptotic expansion -/// Begin_Latex -/// #frac{d}{dx} Ber(x) = M cos#left(#theta - #frac{#pi}{4}#right) -/// End_Latex -/// See also M(x) and Theta(x). +/// \f[ +/// \frac{d}{dx} Ber(x) = M cos\left(\theta - \frac{\pi}{4}\right) +/// \f] +/// See also M() and Theta(). /// /// Begin_Macro /// { @@ -343,10 +344,10 @@ /// If x < fgMin (=20), DBei(x) is computed according to the derivative of /// the polynomial approximation of Bei(x). Otherwise it is computed /// according to its asymptotic expansion -/// Begin_Latex -/// #frac{d}{dx} Bei(x) = M sin#left(#theta - #frac{#pi}{4}#right) -/// End_Latex -/// See also M(x) and Theta(x). +/// \f[ +/// \frac{d}{dx} Bei(x) = M sin\left(\theta - \frac{\pi}{4}\right) +/// \f] +/// See also M() and Theta(). /// /// Begin_Macro /// { @@ -388,10 +389,10 @@ /// If x < fgMin (=20), DKer(x) is computed according to the derivative of /// the polynomial approximation of Ker(x). Otherwise it is computed /// according to its asymptotic expansion -/// Begin_Latex -/// #frac{d}{dx} Ker(x) = N cos#left(#phi - #frac{#pi}{4}#right) -/// End_Latex -/// See also N(x) and Phi(x). +/// \f[ +/// \frac{d}{dx} Ker(x) = N cos\left(\phi - \frac{\pi}{4}\right) +/// \f] +/// See also N() and Phi(). /// /// Begin_Macro /// { @@ -436,10 +437,10 @@ /// If x < fgMin (=20), DKei(x) is computed according to the derivative of /// the polynomial approximation of Kei(x). Otherwise it is computed /// according to its asymptotic expansion -/// Begin_Latex -/// #frac{d}{dx} Kei(x) = N sin#left(#phi - #frac{#pi}{4}#right) -/// End_Latex -/// See also N(x) and Phi(x). +/// \f[ +/// \frac{d}{dx} Kei(x) = N sin\left(\phi - \frac{\pi}{4}\right) +/// \f] +/// See also N() and Phi(). /// /// Begin_Macro /// { @@ -481,9 +482,9 @@ //////////////////////////////////////////////////////////////////////////////// /// Utility function appearing in the calculations of the Kelvin /// functions Bei(x) and Ber(x) (and their derivatives). F1(x) is given by -/// Begin_Latex -/// F1(x) = 1 + #sum_{n #geq 1} #frac{#prod_{m=1}^{n}(2m - 1)^{2}}{n! (8x)^{n}} cos#left(#frac{n#pi}{4}#right) -/// End_Latex +/// \f[ +/// F1(x) = 1 + \sum_{n \geq 1} \frac{\prod_{m=1}^{n}(2m - 1)^{2}}{n! (8x)^{n}} cos\left(\frac{n\pi}{4}\right) +/// \f] double KelvinFunctions::F1(double x) { @@ -510,9 +511,9 @@ //////////////////////////////////////////////////////////////////////////////// /// Utility function appearing in the calculations of the Kelvin /// functions Kei(x) and Ker(x) (and their derivatives). F2(x) is given by -/// Begin_Latex -/// F2(x) = 1 + #sum_{n #geq 1} (-1)^{n} #frac{#prod_{m=1}^{n}(2m - 1)^{2}}{n! (8x)^{n}} cos#left(#frac{n#pi}{4}#right) -/// End_Latex +/// \f[ +/// F2(x) = 1 + \sum_{n \geq 1} (-1)^{n} \frac{\prod_{m=1}^{n}(2m - 1)^{2}}{n! (8x)^{n}} cos\left(\frac{n\pi}{4}\right) +/// \f] double KelvinFunctions::F2(double x) { @@ -541,9 +542,9 @@ //////////////////////////////////////////////////////////////////////////////// /// Utility function appearing in the calculations of the Kelvin /// functions Bei(x) and Ber(x) (and their derivatives). G1(x) is given by -/// Begin_Latex -/// G1(x) = #sum_{n #geq 1} #frac{#prod_{m=1}^{n}(2m - 1)^{2}}{n! (8x)^{n}} sin#left(#frac{n#pi}{4}#right) -/// End_Latex +/// \f[ +/// G1(x) = \sum_{n \geq 1} \frac{\prod_{m=1}^{n}(2m - 1)^{2}}{n! (8x)^{n}} sin\left(\frac{n\pi}{4}\right) +/// \f] double KelvinFunctions::G1(double x) { @@ -568,9 +569,9 @@ //////////////////////////////////////////////////////////////////////////////// /// Utility function appearing in the calculations of the Kelvin /// functions Kei(x) and Ker(x) (and their derivatives). G2(x) is given by -/// Begin_Latex -/// G2(x) = #sum_{n #geq 1} (-1)^{n} #frac{#prod_{m=1}^{n}(2m - 1)^{2}}{n! (8x)^{n}} sin#left(#frac{n#pi}{4}#right) -/// End_Latex +/// \f[ +/// G2(x) = \sum_{n \geq 1} (-1)^{n} \frac{\prod_{m=1}^{n}(2m - 1)^{2}}{n! (8x)^{n}} sin\left(\frac{n\pi}{4}\right) +/// \f] double KelvinFunctions::G2(double x) { @@ -597,9 +598,9 @@ //////////////////////////////////////////////////////////////////////////////// /// Utility function appearing in the asymptotic expansions of DBer(x) and /// DBei(x). M(x) is given by -/// Begin_Latex -/// M(x) = #frac{e^{x/#sqrt{2}}}{#sqrt{2#pix}}#left(1 + #frac{1}{8#sqrt{2} x} + #frac{1}{256 x^{2}} - #frac{399}{6144#sqrt{2} x^{3}} + O#left(#frac{1}{x^{4}}#right)#right) -/// End_Latex +/// \f[ +/// M(x) = \frac{e^{x/\sqrt{2}}}{\sqrt{2\pi x}}\left(1 + \frac{1}{8\sqrt{2} x} + \frac{1}{256 x^{2}} - \frac{399}{6144\sqrt{2} x^{3}} + O\left(\frac{1}{x^{4}}\right)\right) +/// \f] double KelvinFunctions::M(double x) { @@ -612,10 +613,10 @@ //////////////////////////////////////////////////////////////////////////////// /// Utility function appearing in the asymptotic expansions of DBer(x) and -/// DBei(x). Begin_Latex #theta(x) #End_Latex is given by -/// Begin_Latex -/// #theta(x) = #frac{x}{#sqrt{2}} - #frac{#pi}{8} - #frac{1}{8#sqrt{2} x} - #frac{1}{16 x^{2}} - #frac{25}{384#sqrt{2} x^{3}} + O#left(#frac{1}{x^{5}}#right) -/// End_Latex +/// DBei(x). \f$\theta(x)\f$ is given by +/// \f[ +/// \theta(x) = \frac{x}{\sqrt{2}} - \frac{\pi}{8} - \frac{1}{8\sqrt{2} x} - \frac{1}{16 x^{2}} - \frac{25}{384\sqrt{2} x^{3}} + O\left(\frac{1}{x^{5}}\right) +/// \f] double KelvinFunctions::Theta(double x) { @@ -628,10 +629,10 @@ //////////////////////////////////////////////////////////////////////////////// /// Utility function appearing in the asymptotic expansions of DKer(x) and -/// DKei(x). (x) is given by -/// Begin_Latex -/// N(x) = #sqrt{#frac{#pi}{2x}} e^{-x/#sqrt{2}} #left(1 - #frac{1}{8#sqrt{2} x} + #frac{1}{256 x^{2}} + #frac{399}{6144#sqrt{2} x^{3}} + O#left(#frac{1}{x^{4}}#right)#right) -/// End_Latex +/// DKei(x). N(x) is given by +/// \f[ +/// N(x) = \sqrt{\frac{\pi}{2x}} e^{-x/\sqrt{2}} \left(1 - \frac{1}{8\sqrt{2} x} + \frac{1}{256 x^{2}} + \frac{399}{6144\sqrt{2} x^{3}} + O\left(\frac{1}{x^{4}}\right)\right) +/// \f] double KelvinFunctions::N(double x) { @@ -644,10 +645,10 @@ //////////////////////////////////////////////////////////////////////////////// /// Utility function appearing in the asymptotic expansions of DKer(x) and -/// DKei(x). Begin_Latex #phi(x) #End_Latex is given by -/// Begin_Latex -/// #phi(x) = - #frac{x}{#sqrt{2}} - #frac{#pi}{8} + #frac{1}{8#sqrt{2} x} - #frac{1}{16 x^{2}} + #frac{25}{384#sqrt{2} x^{3}} + O#left(#frac{1}{x^{5}}#right) -/// End_Latex +/// DKei(x). \f$\phi(x)\f$ is given by +/// \f[ +/// \phi(x) = - \frac{x}{\sqrt{2}} - \frac{\pi}{8} + \frac{1}{8\sqrt{2} x} - \frac{1}{16 x^{2}} + \frac{25}{384\sqrt{2} x^{3}} + O\left(\frac{1}{x^{5}}\right) +/// \f] double KelvinFunctions::Phi(double x) { diff -ur root-6.06.02.orig/roofit/roostats/inc/RooStats/HybridResult.h root-6.06.02/roofit/roostats/inc/RooStats/HybridResult.h --- root-6.06.02.orig/roofit/roostats/inc/RooStats/HybridResult.h 2016-03-03 10:36:03.000000000 +0100 +++ root-6.06.02/roofit/roostats/inc/RooStats/HybridResult.h 2016-03-20 18:30:30.945025834 +0100 @@ -85,7 +85,7 @@ /// The error on the "confidence level" of the alternative hypothesis Double_t CLsplusbError() const; - /// The error on the ratio CLs+b/CLb + /// The error on the ratio \f$CL_{s+b}/CL_{b}\f$ Double_t CLsError() const; private: diff -ur root-6.06.02.orig/roofit/roostats/inc/RooStats/HypoTestResult.h root-6.06.02/roofit/roostats/inc/RooStats/HypoTestResult.h --- root-6.06.02.orig/roofit/roostats/inc/RooStats/HypoTestResult.h 2016-03-03 10:36:03.000000000 +0100 +++ root-6.06.02/roofit/roostats/inc/RooStats/HypoTestResult.h 2016-03-20 18:30:30.972026102 +0100 @@ -37,11 +37,12 @@ Any tool inheriting from HypoTestCalculator can return a HypoTestResult. As such, it stores a p-value for the null-hypothesis (eg. background-only) and an alternate hypothesis (eg. signal+background). - The p-values can also be transformed into confidence levels (CLb, CLsplusb) in a trivial way. - The ratio of the CLsplusb to CLb is often called CLs, and is considered useful, though it is - not a probability. - Finally, the p-value of the null can be transformed into a number of equivalent Gaussian sigma using the - Significance method. + The p-values can also be transformed into confidence levels + (\f$CL_{b}\f$, \f$CL_{s+b}\f$) in a trivial way. + The ratio of the \f$CL_{s+b}\f$ to \f$CL_{b}\f$ is often called + \f$CL_{s}\f$, and is considered useful, though it is not a probability. + Finally, the p-value of the null can be transformed into a number of + equivalent Gaussian sigma using the Significance method. The p-value of the null for a given test statistic is rigorously defined and this is the starting point for the following conventions. @@ -52,17 +53,17 @@ observed value of the test statistic. This is the more standard convention and avoids confusion when doing inverted tests. -For exclusion, we also want the formula -CLs = CLs+b / CLb to hold which therefore defines our conventions -for CLs+b and CLb. CLs was specifically invented for exclusion +For exclusion, we also want the formula \f$CL_{s} = CL_{s+b} / CL_{b}\f$ +to hold which therefore defines our conventions for \f$CL_{s+b}\f$ and +\f$CL_{b}\f$. \f$CL_{s}\f$ was specifically invented for exclusion and therefore all quantities need be related through the assignments -as they are for exclusion: **CLs+b = p_{s+b}; CLb = p_b**. This +as they are for exclusion: \f$CL_{s+b} = p_{s+b}\f$; \f$CL_{b} = p_{b}\f$. This is derived by considering the scenarios of a powerful and not powerful -inverted test, where for the not so powerful test, CLs must be +inverted test, where for the not so powerful test, \f$CL_{s}\f$ must be close to one. For results of Hypothesis tests, -CLs has no similar direct interpretation as for exclusion and can +\f$CL_{s}\f$ has no similar direct interpretation as for exclusion and can be larger than one. */ @@ -101,7 +102,7 @@ /// Convert AlternatePValue into a "confidence level" virtual Double_t CLsplusb() const { return !fBackgroundIsAlt ? AlternatePValue() : NullPValue(); } - /// CLs is simply CLs+b/CLb (not a method, but a quantity) + /// \f$CL_{s}\f$ is simply \f$CL_{s+b}/CL_{b}\f$ (not a method, but a quantity) virtual Double_t CLs() const { double thisCLb = CLb(); if (thisCLb == 0) { @@ -144,7 +145,7 @@ /// The error on the "confidence level" of the alternative hypothesis Double_t CLsplusbError() const; - /// The error on the ratio CLs+b/CLb + /// The error on the ratio \f$CL_{s+b}/CL_{b}\f$ Double_t CLsError() const; /// The error on the Null p-value diff -ur root-6.06.02.orig/roofit/roostats/src/HybridResult.cxx root-6.06.02/roofit/roostats/src/HybridResult.cxx --- root-6.06.02.orig/roofit/roostats/src/HybridResult.cxx 2016-03-03 10:36:03.000000000 +0100 +++ root-6.06.02/roofit/roostats/src/HybridResult.cxx 2016-03-20 18:30:30.973026112 +0100 @@ -100,11 +100,9 @@ } /////////////////////////////////////////////////////////////////////////// - +/// Returns \f$1 - CL_{b}\f$ : the B p-value double HybridResult::NullPValue() const { - // return 1-CL_b : the B p-value - if (fComputationsNulDoneFlag==false) { int nToys = fTestStat_b.size(); if (nToys==0) { @@ -131,11 +129,9 @@ } /////////////////////////////////////////////////////////////////////////// - +/// Returns \f$CL_{s+b}\f$ : the S+B p-value double HybridResult::AlternatePValue() const { - // return CL_s+b : the S+B p-value - if (fComputationsAltDoneFlag==false) { int nToys = fTestStat_b.size(); if (nToys==0) { @@ -162,40 +158,37 @@ } /////////////////////////////////////////////////////////////////////////// - +/// Returns an estimate of the error on \f$CL_{b}\f$ assuming a binomial +/// error on \f$CL_{b}\f$: +/// \f[ +/// \sigma_{CL_{b}} = \sqrt{CL_{b} \left( 1 - CL_{b} \right) / n_{toys}} +/// \f] Double_t HybridResult::CLbError() const { - // Returns an estimate of the error on CLb assuming a binomial error on - // CLb: - // BEGIN_LATEX - // #sigma_{CL_{b}} &=& #sqrt{CL_{b} #left( 1 - CL_{b} #right) / n_{toys}} - // END_LATEX unsigned const int n = fTestStat_b.size(); return TMath::Sqrt(CLb() * (1. - CLb()) / n); } /////////////////////////////////////////////////////////////////////////// - +/// Returns an estimate of the error on \f$CL_{s+b}\f$ assuming a binomial +/// error on \f$CL_{s+b}\f$: +/// \f[ +/// \sigma_{CL_{s+b}} = \sqrt{CL_{s+b} \left( 1 - CL_{s+b} \right) / n_{toys}} +/// \f] Double_t HybridResult::CLsplusbError() const { - // Returns an estimate of the error on CLsplusb assuming a binomial - // error on CLsplusb: - // BEGIN_LATEX - // #sigma_{CL_{s+b}} &=& #sqrt{CL_{s+b} #left( 1 - CL_{s+b} #right) / n_{toys}} - // END_LATEX unsigned const int n = fTestStat_sb.size(); return TMath::Sqrt(CLsplusb() * (1. - CLsplusb()) / n); } /////////////////////////////////////////////////////////////////////////// - +/// Returns an estimate of the error on \f$CL_{s}\f$ through combination +/// of the errors on \f$CL_{b}\f$ and \f$CL_{s+b}\f$: +/// \f[ +/// \sigma_{CL_s} = CL_s \sqrt{\left( \frac{\sigma_{CL_{s+b}}}{CL_{s+b}} \right)^2 + \left( \frac{\sigma_{CL_{b}}}{CL_{b}} \right)^2} +/// \f] Double_t HybridResult::CLsError() const { - // Returns an estimate of the error on CLs through combination of the - // errors on CLb and CLsplusb: - // BEGIN_LATEX - // #sigma_{CL_s} &=& CL_s #sqrt{#left( #frac{#sigma_{CL_{s+b}}}{CL_{s+b}} #right)^2 + #left( #frac{#sigma_{CL_{b}}}{CL_{b}} #right)^2} - // END_LATEX unsigned const int n_b = fTestStat_b.size(); unsigned const int n_sb = fTestStat_sb.size(); diff -ur root-6.06.02.orig/roofit/roostats/src/HypoTestResult.cxx root-6.06.02/roofit/roostats/src/HypoTestResult.cxx --- root-6.06.02.orig/roofit/roostats/src/HypoTestResult.cxx 2016-03-03 10:36:03.000000000 +0100 +++ root-6.06.02/roofit/roostats/src/HypoTestResult.cxx 2016-03-20 18:30:30.973026112 +0100 @@ -229,8 +229,8 @@ } //////////////////////////////////////////////////////////////////////////////// -/// compute CLb error -/// Clb = 1 - NullPValue() +/// compute \f$CL_{b}\f$ error +/// \f$CL_{b}\f$ = 1 - NullPValue() /// must use opposite condition that routine above Double_t HypoTestResult::CLbError() const { @@ -251,12 +251,12 @@ } //////////////////////////////////////////////////////////////////////////////// -/// Returns an estimate of the error on CLs through combination of the -/// errors on CLb and CLsplusb: -/// BEGIN_LATEX -/// #sigma_{CL_s} = CL_s -/// #sqrt{#left( #frac{#sigma_{CL_{s+b}}}{CL_{s+b}} #right)^2 + #left( #frac{#sigma_{CL_{b}}}{CL_{b}} #right)^2} -/// END_LATEX +/// Returns an estimate of the error on \f$CL_{s}\f$ through combination of the +/// errors on \f$CL_{b}\f$ and \f$CL_{s+b}\f$: +/// \f[ +/// \sigma_{CL_s} = CL_s +/// \sqrt{\left( \frac{\sigma_{CL_{s+b}}}{CL_{s+b}} \right)^2 + \left( \frac{\sigma_{CL_{b}}}{CL_{b}} \right)^2} +/// \f] Double_t HypoTestResult::CLsError() const { if(!fAltDistr || !fNullDistr) return 0.0;