\contentsline {section}{\numberline {1}Introduction}{1}{section.1}% 
\contentsline {section}{\numberline {2}Model fitting}{5}{section.2}% 
\contentsline {subsection}{\numberline {2.1}Maximum Likelihood}{5}{subsection.2.1}% 
\contentsline {subsection}{\numberline {2.2}Requirements}{6}{subsection.2.2}% 
\contentsline {subsection}{\numberline {2.3}Existing libraries}{7}{subsection.2.3}% 
\contentsline {subsubsection}{\numberline {2.3.1}General fitting}{7}{subsubsection.2.3.1}% 
\contentsline {subsubsection}{\numberline {2.3.2}HEP specific}{8}{subsubsection.2.3.2}% 
\contentsline {section}{\numberline {3}\texttt {zfit}{} introduction}{10}{section.3}% 
\contentsline {subsection}{\numberline {3.1}TensorFlow backend}{12}{subsection.3.1}% 
\contentsline {section}{\numberline {4}\texttt {zfit}{} implementation}{17}{section.4}% 
\contentsline {subsection}{\numberline {4.1}Spaces and Dimensions}{18}{subsection.4.1}% 
\contentsline {subsubsection}{\numberline {4.1.1}Limits}{18}{subsubsection.4.1.1}% 
\contentsline {subsection}{\numberline {4.2}Data handling}{19}{subsection.4.2}% 
\contentsline {subsection}{\numberline {4.3}Model}{20}{subsection.4.3}% 
\contentsline {subsubsection}{\numberline {4.3.1}Parametrization}{21}{subsubsection.4.3.1}% 
\contentsline {subsubsection}{\numberline {4.3.2}Implementing a custom PDF}{22}{subsubsection.4.3.2}% 
\contentsline {subsubsection}{\numberline {4.3.3}Sampling}{25}{subsubsection.4.3.3}% 
\contentsline {subsubsection}{\numberline {4.3.4}Extended PDFs}{26}{subsubsection.4.3.4}% 
\contentsline {subsection}{\numberline {4.4}Loss}{26}{subsection.4.4}% 
\contentsline {subsection}{\numberline {4.5}Minimisation}{28}{subsection.4.5}% 
\contentsline {subsubsection}{\numberline {4.5.1}Different optimisations}{28}{subsubsection.4.5.1}% 
\contentsline {subsection}{\numberline {4.6}Results and uncertainties}{29}{subsection.4.6}% 
\contentsline {subsubsection}{\numberline {4.6.1}Parameter uncertainties}{30}{subsubsection.4.6.1}% 
\contentsline {section}{\numberline {5}Performance}{31}{section.5}% 
\contentsline {subsection}{\numberline {5.1}Gaussian models}{31}{subsection.5.1}% 
\contentsline {subsection}{\numberline {5.2}Angular analysis}{34}{subsection.5.2}% 
\contentsline {section}{\numberline {6}Beyond standard fitting}{36}{section.6}% 
\contentsline {subsection}{\numberline {6.1}Amplitude fits}{37}{subsection.6.1}% 
\contentsline {subsection}{\numberline {6.2}phasespace}{38}{subsection.6.2}% 
\contentsline {subsection}{\numberline {6.3}Dalitz implementation}{39}{subsection.6.3}% 
\contentsline {section}{\numberline {7}Conclusion and outlook}{44}{section.7}% 
\contentsline {section}{\numberline {A}Likelihood}{47}{appendix.A}% 
\contentsline {section}{\numberline {B}Backend}{50}{appendix.B}% 
\contentsline {subsection}{\numberline {B.1}HPC and paradigms}{50}{subsection.B.1}% 
\contentsline {subsection}{\numberline {B.2}Working with TensorFlow}{52}{subsection.B.2}% 
\contentsline {subsubsection}{\numberline {B.2.1}Caching}{53}{subsubsection.B.2.1}% 
\contentsline {section}{\numberline {C}Implementation}{54}{appendix.C}% 
\contentsline {subsection}{\numberline {C.1}Spaces definition}{54}{subsection.C.1}% 
\contentsline {subsection}{\numberline {C.2}General limits}{55}{subsection.C.2}% 
\contentsline {subsection}{\numberline {C.3}Data formats}{56}{subsection.C.3}% 
\contentsline {subsection}{\numberline {C.4}Data batching}{57}{subsection.C.4}% 
\contentsline {subsection}{\numberline {C.5}Dependency management}{57}{subsection.C.5}% 
\contentsline {subsection}{\numberline {C.6}Base Model}{58}{subsection.C.6}% 
\contentsline {subsubsection}{\numberline {C.6.1}Public methods}{58}{subsubsection.C.6.1}% 
\contentsline {subsubsection}{\numberline {C.6.2}Hooks}{59}{subsubsection.C.6.2}% 
\contentsline {subsubsection}{\numberline {C.6.3}Norm range handling}{59}{subsubsection.C.6.3}% 
\contentsline {subsubsection}{\numberline {C.6.4}Multiple limits handling}{60}{subsubsection.C.6.4}% 
\contentsline {subsubsection}{\numberline {C.6.5}Most efficient method}{60}{subsubsection.C.6.5}% 
\contentsline {subsubsection}{\numberline {C.6.6}Functors}{61}{subsubsection.C.6.6}% 
\contentsline {subsection}{\numberline {C.7}Sampling techniques}{61}{subsection.C.7}% 
\contentsline {subsection}{\numberline {C.8}Loss defined}{63}{subsection.C.8}% 
\contentsline {section}{\numberline {D}Performance studies}{63}{appendix.D}% 
\contentsline {subsection}{\numberline {D.1}Hardware specification}{63}{subsection.D.1}% 
\contentsline {subsection}{\numberline {D.2}Profiling TensorFlow}{64}{subsection.D.2}% 
\contentsline {subsection}{\numberline {D.3}Additional profiling}{65}{subsection.D.3}% 
\contentsline {section}{References}{65}{figure.caption.18}%