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\author{Jihyun Bhom (IFJ PAN), Marcin Chrzaszcz (CERN)}
\institute{UZH}
\title[HEPLike]{HEPLike}
\begin{document}
\tikzstyle{every picture}+=[remember picture]
{
\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}}
\begin{frame}[c]%{\phantom{title page}}
\begin{center}
\begin{center}
\begin{columns}
\begin{column}{0.15\textwidth}
{~}
\end{column}
\begin{column}{0.02\textwidth}
{~}
\end{column}
\begin{column}{0.73\textwidth}
\flushright \bfseries \Large {HEPLike - tool for experimental likelihood evaluation}
\end{column}
\begin{column}{0.02\textwidth}
{~}
\end{column}
\end{columns}
\end{center}
\quad
\vspace{3em}
\begin{columns}
\begin{column}{0.44\textwidth}
\flushright \vspace{-2.8em} {Jihyun Bhom\\ \small \href{mailto:jihyun.bohm@cern.ch}{jihyun.bohm@cern.ch} \vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}\\ Marcin Chrzaszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
%\flushright \vspace{-2.8em} { Marcin Chrzaszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
\end{column}
\begin{column}{0.53\textwidth}
\hspace{2.0cm}
\includegraphics[height=1.6cm]{cern}{~}
\includegraphics[height=1.6cm]{ifj.png}
\end{column}
\end{columns}
\vspace{1em}
\vspace{1.4cm}
\textcolor{normal text.fg!50!Comment}{(Re)interpreting the results of new physics searches at the LHC, London, April 2-4, 2019}
\end{center}
\end{frame}
}
\begin{frame}\frametitle{HEP results}
\ARROW How do we publish results?
\begin{columns}
\column{0.35\textwidth}
\includegraphics[width=0.95\textwidth]{images/arxiv.png}\\
\pause
\begin{align*}
R_K=0.846^{+0.060 +0.016}_{-0.054 - 0.014}
\end{align*}
\pause
\column{0.65\textwidth}
\begin{center}
\includegraphics[angle=-90,width=0.5\textwidth]{images/FigS8.pdf}\\
\pause
\includegraphics[width=0.75\textwidth]{images/hepdata.png}
\end{center}
\end{columns}
\end{frame}
\begin{frame}\frametitle{HEP results}
\ARROW How are the results used?
\begin{columns}
\column{0.5\textwidth}
\ARROWR Correlations are neglected
\includegraphics[width=0.75\textwidth]{{images/Table_12}.pdf}
\ARROWR Non Linear effects are forgotten
\includegraphics[angle=-90,width=0.75\textwidth]{{images/example}.pdf}
\column{0.5\textwidth}
\ARROWR Errors are being symmetrized
\includegraphics[angle=-90,width=0.75\textwidth]{{images/Fig62aS}.pdf}
{~}\\{~}\\
\end{columns}
\end{frame}
\begin{frame}\frametitle{HEP results}
\ARROW How are the results used?\\{~}\\
\ARROWR Interpreting Upper limits [HLFAV, 90\% UL]:
\begin{align*}
\mathcal{B} (\tau \to \mu \mu e) < 9.9 \times 10^{-9}
\end{align*}
\ARROW People interpret this assuming it's a gaussian centered around $0$ and width $\frac{9.9\times 10^{-9}}{1.64} $.\\
\ARROW Usually a full p-value scan is published:
\begin{columns}
\column{0.5\textwidth}
\includegraphics[width=0.75\textwidth]{{images/180}.png}
\column{0.5\textwidth}
\includegraphics[width=0.75\textwidth]{{images/dupa}.png}
\end{columns}
\ARROW The examples go on and on...
\end{frame}
\begin{frame}\frametitle{The idea}
\ARROW The theory and experimental community need to work together about proper interpretation.
\pause
\begin{center}
\includegraphics[width=0.95\textwidth]{{images/kim}.jpg}
\end{center}
\end{frame}
\begin{frame}\frametitle{HEPLike}
\ARROW High Energy Physics Likelihood (HEPLike).
\begin{itemize}
\item Open source software.
\item With separate database of measurements.
\item Statistics library.
\item Can be interfaced with existing codes.
\end{itemize}
\ARROW It constructs the experimental likelihoods for you!\\
\ARROW Does work with both the $\chi^2$ and (log-)likelihood fits.\\
\ARROW Useful utilities for creating citations and database search.
\end{frame}
\begin{frame}\frametitle{HEPLike}
\ARROW The are couple of measurement types:
\begin{itemize}
\item Upper limits,
\item Single measurement with symmetric uncertainty,
\item Single measurement with asymmetric uncertainty,
\item Multiple measurements with symmetric uncertainty,
\item Multiple measurements with asymmetric uncertainty,
\item One dimensional likelihood function,
\item n-dimensional likelihood function.
\end{itemize}
\begin{alertblock}{Bonus}
In addition we provide a way for the future that the experiments can publish the dataset.
\end{alertblock}
\end{frame}
\begin{frame}\frametitle{HEPLike - code structure}
\begin{center}
\includegraphics[width=0.99\textwidth]{images/diagram.png}
\end{center}
\end{frame}
\begin{frame}\frametitle{Measurement encoding, \texttt{Hl\_Data}}
\ARROW Measurements are stored in \texttt{YAML} file:
\includegraphics[width=0.9\textwidth]{images/yaml.png} \\
\includegraphics[width=0.9\textwidth]{images/yaml2.png}
\end{frame}
\begin{frame}\frametitle{Upper limits, \texttt{HL\_Limit}}
\ARROW Example of published p-value scans:\\
\begin{columns}
\column{0.4\textwidth}
\includegraphics[angle=-90,width=0.95\textwidth]{images/Bs2tautau.pdf}
\column{0.6\textwidth}
\ARROW Information coded as:
\includegraphics[width=0.95\textwidth]{images/yaml3.png}
\end{columns}
\end{frame}
\begin{frame}\frametitle{Upper limits, \texttt{HL\_Limit}}
\begin{equation}
pdf(x) = \frac{1}{2^{1/2} \Gamma(1/2)} x^{1/2 -1} e ^{-x/2},
\end{equation}
which had the cumulative distribution function defined as:
\begin{equation}
cdf(x)=\frac{1}{\Gamma(1/2) } \gamma(1/2,x/2).
\end{equation}
In the above equations the $\Gamma(x)$ and $\gamma(k,x)$ correspond to Gamma and incomplete gamma functions.
By revering the $cdf(x)$ one can obtain the $\chi^2$ value:
\begin{equation}
\chi^2=cdf^{-1}(1-p),
\end{equation}
and if needed the log-likelihood:
\begin{equation}
-\log(\mathcal{L})= \frac{1}{2}\chi^2, \label{eq:wilks}
\end{equation}
\end{frame}
\begin{frame}\frametitle{Single measurement, symmetric error, \texttt{HL\_Gaussian}}
\end{frame}
\backupbegin
\begin{frame}\frametitle{Backup}
\topline
\end{frame}
\backupend
\end{document}
Marcin Chrzaszcz