\relax \citation{asimov} \citation{asimov} \citation{asimov} \@writefile{toc}{\contentsline {section}{\numberline {1}Introduction}{2}} \newlabel{sec:intro}{{1}{2}} \newlabel{eq:Zval}{{1}{2}} \@writefile{toc}{\contentsline {section}{\numberline {2}Discovery as a statistical test}{2}} \newlabel{sec:disctest}{{2}{2}} \newlabel{eq:PLR}{{2}{2}} \citation{asimov} \newlabel{eq:q0}{{3}{3}} \@writefile{toc}{\contentsline {section}{\numberline {3}$s/\sqrt {b}$ and related measures of discovery sensitivity}{3}} \newlabel{sec:soverrootb}{{3}{3}} \newlabel{eq:pvalx}{{4}{3}} \newlabel{eq:Zx}{{5}{3}} \newlabel{eq:soverrootb}{{6}{3}} \newlabel{eq:soverrootbsys}{{7}{3}} \citation{asimov} \citation{asimov} \citation{asimov} \citation{asimov} \citation{CowanPhystatAsimov} \citation{asimov} \citation{CowanPhystatAsimov} \citation{asimov} \citation{CowanPhystatAsimov} \@writefile{toc}{\contentsline {section}{\numberline {4}Poisson case with known background}{4}} \newlabel{sec:bknown}{{4}{4}} \newlabel{eq:poissonL}{{8}{4}} \newlabel{eq:Z0count}{{9}{4}} \newlabel{eq:Zmedcount}{{10}{4}} \newlabel{eq:Zmedcount2}{{11}{4}} \citation{asimov} \citation{LiMa83} \citation{Cranmer05} \citation{Cousins08} \@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces {\relax \fontsize {9}{11}\selectfont \abovedisplayskip 8\p@ plus2\p@ minus4\p@ \abovedisplayshortskip \z@ plus\p@ \belowdisplayshortskip 4\p@ plus2\p@ minus2\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 4\p@ plus2\p@ minus2\p@ \parsep 2\p@ plus\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip The median, assuming a mean number of signal events $s$, of the discovery significance $Z$ for different values of $s$ and $b$ (from \cite {asimov,CowanPhystatAsimov}; see text).} \label {fig:medsig}}}{5}} \newlabel{fig:medsig}{{1}{5}} \@writefile{toc}{\contentsline {section}{\numberline {5}Poisson case with uncertain background}{5}} \newlabel{sec:bunknown}{{5}{5}} \newlabel{eq:onoffL}{{12}{5}} \newlabel{eq:shat}{{13}{5}} \newlabel{eq:bhat}{{14}{5}} \newlabel{eq:bhathat}{{15}{5}} \newlabel{eq:bhathat0}{{16}{5}} \citation{LiMa83} \citation{Cousins08} \newlabel{eq:onoffZ}{{17}{6}} \newlabel{eq:onoffmedZ}{{18}{6}} \newlabel{eq:sigma2b}{{19}{6}} \newlabel{eq:onoffmedZ2}{{20}{6}} \newlabel{eq:onoffmedZ3}{{21}{6}} \@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces \relax \fontsize {10}{12}\selectfont \abovedisplayskip 10\p@ plus2\p@ minus5\p@ \abovedisplayshortskip \z@ plus3\p@ \belowdisplayshortskip 6\p@ plus3\p@ minus3\p@ \def \leftmargin \leftmargini \parsep 4.5\p@ plus2\p@ minus\p@ \topsep 9\p@ plus3\p@ minus5\p@ \itemsep 4.5\p@ plus2\p@ minus\p@ {\leftmargin \leftmargini \topsep 6\p@ plus2\p@ minus2\p@ \parsep 3\p@ plus2\p@ minus\p@ \itemsep \parsep }\belowdisplayskip \abovedisplayskip The median, assuming an expected number of signal events $s = 2, 5$ and $10$ of the discovery significance $Z$ as a function of the expected number of background events $b$ for (left) several values of $\sigma _b/b$ and (right) several values of $\tau $ (see text).}}{7}} \newlabel{fig:medsigsys}{{2}{7}} \bibcite{asimov}{1} \bibcite{CowanPhystatAsimov}{2} \citation{asimov} \bibcite{LiMa83}{3} \bibcite{Cranmer05}{4} \bibcite{Cousins08}{5} \@writefile{toc}{\contentsline {section}{\numberline {6}Conclusions}{8}} \newlabel{sec:conclusions}{{6}{8}}