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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)}
\institute{UZH}
\title[Entia non sunt multiplicanda praeter necessitatem - $\PB \to \PKstar \Pmuon \APmuon$]{Entia non sunt multiplicanda praeter necessitatem - $\PB \to \PKstar \Pmuon \APmuon$}
\date{25 September 2014}


\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}{0.9\textwidth}
			\flushright\fontspec{Trebuchet MS}\bfseries \Huge {Entia non sunt multiplicanda praeter necessitatem \\ aka $\PB \to \PKstar \Pmuon \APmuon$}
		\end{column}
		\begin{column}{0.2\textwidth}
		  %\includegraphics[width=\textwidth]{SHiP-2}
		\end{column}
	\end{columns}
\end{center}
	\quad
	\vspace{3em}
\begin{columns}
\begin{column}{0.44\textwidth}
\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}

\end{column}
\begin{column}{0.53\textwidth}
\includegraphics[height=1.3cm]{uzh-transp}
\end{column}
\end{columns}

\vspace{1em}
%		\footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\
\vspace{0.5em}
	\textcolor{normal text.fg!50!Comment}{Zurich meeting, CERN\\September 24, 2014}
\end{center}
\end{frame}
}


\begin{frame}[c]{Many paths...}
\begin{itemize}
\item Jacobian transformation 
\item Profile likelihoods 
\item Quantiles 
\end{itemize}


\end{frame}


\begin{frame}[c]{Jacobian transformation }
\begin{itemize}                                                                                                                                              
\item Now how does the new space look like.                                                                                                                  
\item Important to take into account the boundary as without all my theorems fall down.                                                                      
\item The white point is the value from which the toy was generated.                                                                                         
\end{itemize}                                                                                                                                                
\begin{center}                                                                                                                                               
                                                                                                                                                             
\begin{columns}                                                                                                                                              
\column{2.5in}                                                                                                                                               
\begin{small}                                                                                                                                                
Scatter plot $F_L:P_2$, no Jacobian                                                                                                                          
\end{small}                                                                                                                                                  
                                                                                                                                                             
\column{0.5in}                                                                                                                                               
{~}                                                                                                                                                          
\column{2.2in}                                                                                                                                               
                                                                                                                                                             
\begin{small}                                                                                                                                                
Scatter plot $F_L:P_2$, with Jacobian                                                                                                                        
\end{small}                                                                                                                                                  
                                                                                                                                                             
\end{columns}                                                                                                                                                
\includegraphics[width=1.1\textwidth]{images/2DZ2.png}                                                                                                       
                                                                                                                                                             
\end{center}  
                                                                                                                                                             
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Re parametrization of pdf}                                                                                                          



\begin{itemize}                                                                                                                                              
\item Re parametrization of the pdf gives exactly the same answer as toys taking into account the jacobian:                                                  
\end{itemize}                                                                                                                                                
{~}\\{~}\\                                                                                                                                                   
                                                                                                                                                             
\begin{columns}                                                                                                                                              
\column{2.5in}                                                                                                                                               
\begin{small}                                                                                                                                                
Profile likelihood from re-parametrised pdf.                                                                                                                 
\end{small}                                                                                                                                                  
\includegraphics[width=0.9\textwidth]{images/LL_pdf.png}                                                                                                     
\column{2.5in}                                                                                                                                               
\begin{small}                                                                                                                                                
Profile likelihood from toys with Jacobian                                                                                                                   
\end{small}                                                                                                                                                  
\includegraphics[width=0.9\textwidth]{images/LL_toys.png}                                                                                                    
\end{columns}                                                                                                                                                

\end{frame}    



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Profile likelihoods}

\includegraphics[width=0.9\textwidth]{images/profile.png}


\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Quantiles}
\begin{itemize}
\item Apparently quantiles stay invariant under transformations....
\item One can just calculate the $68\%$ around the median.
\item This is our default option :(
\end{itemize}
\only<1>{
\includegraphics[angle=-90,width=0.23\textwidth]{images/S9_4.0_5.0.pdf}
\includegraphics[angle=-90,width=0.23\textwidth]{images/S5_4.0_5.0.pdf}
\includegraphics[angle=-90,width=0.23\textwidth]{images/S8_4.0_5.0.pdf}
\includegraphics[angle=-90,width=0.23\textwidth]{images/S7_4.0_5.0.pdf}
}
\only<2>{
\includegraphics[angle=-90,width=0.23\textwidth]{images/P5_4.0_5.0.pdf}
\includegraphics[angle=-90,width=0.23\textwidth]{images/P4_4.0_5.0.pdf}
\includegraphics[angle=-90,width=0.23\textwidth]{images/P3_4.0_5.0.pdf}
\includegraphics[angle=-90,width=0.23\textwidth]{images/P2_4.0_5.0.pdf}
}


\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{The End?}
\begin{itemize}
\item Tmr we have a meeting with the referees meeting.
\item Ergo bibamus?
\end{itemize}

\end{frame}




\end{document}
