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Slide 1Slide 2Slide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 128.882 LHC PhysicsExperimental Methods and MeasurementsSophisticated Selections: Likelihoods/Neural Networks[Lecture 21, April 27, 2009]C.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 2OrganizationLecture schedule●next week Wednesday replaced with Tuesday at 10:00? Project 2●no additional hand-in yet Project 3●looks fine, people did not have significant questions Conference Schedule●worked outC.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 3Lecture Outline Sophisticate Selections●likelihoods●neural networksC.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 4Sophisticated Selections: Why? Cut based selections●well defined and intuitive selection process●can be optimized from the outside (cut ordering)●simple to implement and monitor●study is straight forward, uncertainties easy●simplistic as each variable has to comply with signal signature, no backup possible More sophisticated methods (likelihoods, ANN etc.)●allow for multidimensional considerations of an event●must be at least as good as cut based analysis●more difficult to comprehend, process and result●study of uncertainties usually more difficult●implementation and optimization less obviousC.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 5Likelihoods as Cut Variables Idea●for each variable has a PDF for signal and background●calculate likelihood for each object to be signal by●so for perfect signal (background) Lsignal = 1 (0) ●each component is given asLsignal = Psignal / (Psignal + Pbackground) Psignal = Psignal,1 * Psignal,2 * ∙∙∙∙Pbackground = Pbackground,1 * Pbackground,2 * ∙∙∙∙C.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 6Signal and Background Distributions Source●grabbed from some CDF presentation●selection for soft muons flavour tagger●red – protons blue – muonsC.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 7Overall Likelihood for MuonsC.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 8Neural Networks From wikipedia:●“Traditionally, the term Neural Network had been used to refer to a network or circuit of biological neurons. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes.”●“Artificial neural networks are made up of interconnecting artificial neurons (programming constructs that mimic the properties of biological neurons). Artificial neural networks may either be used to gain an understanding of biological neural networks, or for solving artificial intelligence problems without necessarily creating a model of a real biological system.”C.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 9Applying an Artificial Neural Network Sample creation●make samples representing signal and background●careful do not train on data you use later●Monte Carlo is easier but often unreliable, study variables●sometimes NN chains needed: muon id, then upsilon id●this is the important step, all depends on the proper samples●train the network on those samples●network returns for each event a number between 0 and 1 corresponding to 0 == background and 1 == signal●apply the trained ANN to the data and decide where to choose the cut on the ANN variable●optimization becomes straight forward●use TMVA class with root... I had not yet the chance to try but it is supposed to be very goodC.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 10Neural Networks For our course●use a pre-packaged ANN implementation: ANN, SNNS, Neurobayes●toolbox very convenient to use for neural nets: TMVAC.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 11Conclusion Sophisticated selections●likelihoods: allow combination of many different variables●variables have predefined signal and background shapes●ANN – Artificial Neural Networks allow combination of many different variables●full signal and background samples have to be provided●training of the network is essential and has various issues●systematic uncertainties are more complex to study with the more complex selection processC.Paus, LHC Physics: Sophisticated Selections: Likelihoods/Neural Networks 12Next Lecture Higgs Searches and Other Essentials●guest lecturer?!●overview over the High pT physics and Higgs searches and some general searches in


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MIT 8 882 - Sophisticated Selections

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