Statistical Methods In Particle Physics - Heidelberg University
Statistical Methods inParticle Physics1. Basics ConceptsProf. Dr. Klaus Reygers (lectures)Dr. Sebastian Neubert (tutorials)Heidelberg UniversityWS 2017/18
IntroductionStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts2
Aims of this Course Statistical inference: from data to knowledge‣ Should a believe a physics claim?‣ Develop intuition‣ Know pitfalls: avoid mistakes already made by others Understand statistical concepts‣ Ability to understand physics papers‣ Know methods / the standard statistical toolbox Use tools‣ Learn to use root‣ Get ready for your own data analysisStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts3
How Knowledge is Created?Guess theory/modelPerform experiment- usually mathematical- self-consistent- simple explanations, few arbitraryparameters- testable predictions / hypotheses- reject / modify theory in case ofdisagreement with data- if theory requires too manyadjustments it becomesunattractiveThe advance of scientific knowledge is anevolutionary processKarl Popper(1902–1994)source: WikipediaStatistical methods are an important part of this processStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts4
Understanding Particle Physics PapersStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts5
A Heavy Higgs Boson?"750 GeV diphoton excess" Two-photon invariantmass spectrum New particle with massm 750 GeV? Local significance: 3.6σPeak disappeared withmore data [link]Presentations by CMS and ATLAS, December al Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts6
This is an Applied Coursehttps://root.cern.ch/ We will use lots of examples from“real life” particle physics We will sometimes talk aboutimplementation on a computer You should ask questions, discuss You will write code (C ), thetutorials will provide a step-by-stepintroduction to rootStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts7
rlesung/20172/smippStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts8
Practical Information (I) Slides of the lecture will be provided on the lecture web site‣ g/20172/smipp‣ Goal: slides available a couple of days before the lecture Weekday/time of the lecture‣ Mondays, 14:15–15:45, KIP SR 3.404‣ There were requests to change the week, but this turned out to be difficult Tutorials‣ Mondays, 16:00–17:30‣ CIP pool of the Physikalisches Institut, not in KIP CIP pool‣ Information on CIP gen/CIP‣ Homework problems will be made available on lecture website‣ Solutions to be handed in by Wednesday, 12:00, of the following week‣ Groups of two students can (actually should!) hand in homework together‣ First homework sheet is available,to be handed in by Wednesday, October 25, 2017, 12:00Statistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts9
Practical Information (II) Exam‣ There will be a written exam at the end of the semester‣ 60% of the points of the homework sheets required to be eligible to write theexam‣ Date to be fixed Successful participating requires to pass the written exam Final grade‣ 2/3 of the points of the homework assignments‣ 1/3 written examStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts10
Useful Reading MaterialBooks: G. Cowan, Statistical Data Analysis L. Lista, Statistical Methods for Data Analysis in Particle Physics Behnke, Kroeninger, Schott, Schoerner-Sadenius: Data Analysis in HighEnergy Physics: A Practical Guide to Statistical Methods R. Barlow, Statistics: A Guide to the Use of Statistical Methods in thePhysical Sciences Bohm, Zech, Introduction to Statistics and Data Analysis for Physicist[available online] Blobel, Lohrmann: Statistische Methoden der Datenanalyse (in German),[free ebook] Lyons:Statistics for Nuclear and Particle Physicists (Cambridge University Press) F. James, Statistical Methods in Experimental physicsStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts11
Further Material Lot's of material from previous lectures by Oleg Brandt at HeidelbergUniversity and others‣ Many thanks! Glen Cowan: http://www.pp.rhul.ac.uk/ cowan/stat course.html Scott Oser: http://www.phas.ubc.ca/ oser/p509/ Particle Data Group reviews on Probability and Statistics [link]Statistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts12
Sources of Uncertainty Underlying theory (quantum mechanics) is probabilistic‣ true randomness Limited knowledge about the measurement process‣ present even without quantum mechanicsWe quantify uncertainty using probabilityStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts13
Mathematical Definition of ProbabilityLet A be an event. Then probability is a number obeyingthree conditions, the Kolmogorov axioms:1. P(A) 0Kolmogorov, 19332. P(S) 1, where S is the set of all A, the sample space3. P(A B) P(A) P(B) for any A, B which are exclusive, i.e., A B 0From these axioms further properties can be derived, e.g.:P(Ā) 1 – P(A)P( ) 0if A B then P(A) P(B)P(A B) P(A) P(B) – P(A B)But what does P mean?Statistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts14
Interpretations of Probability Classical definition‣ Assign equal probabilities based on symmetry of the problem,e.g., rolling dice: P(6) 1/6‣ difficult to generalize Frequentist definition‣ Let A, B, be outcomes of an repeatable experiment:times outcome is AP(A) limn!1n Bayesian definition (subjective probability)‣ A, B, are hypotheses (statements that are true or false)P(A) degree of believe that A is trueAll three definitions are consistent with Kolmogorov's axiomsStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts15
Criticisms of the Probability Interpretations Criticisms of the frequency interpretation‣ n can never be achieved in practice. When is n large enough?‣ We want to talk about the probability of events that are not repeatableExample 1: P(it will rain tomorrow), but there is only one tomorrow- Example 2: P(Universe started with a Big Bang), but only one universe-‣ P is not an intrinsic property of A, it depends on the how the ensemble ofpossible outcomes was constructed-Example: P(person I talk to is a physicist) depends on whether I am in a footballstadium or at a scientific conference Criticisms of the subjective interpretation‣ “Subjective” estimates have no place in science‣ How to quantify the prior state of our knowledge upon which we base ourprobability estimate?"Bayesians address the questions everyone is interested in by usingassumptions that no one believes. Frequentist use impeccable logic todeal with an issue that is of no interest to anyone.” – Louis LyonsStatistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts16
Fun With Probabilitieshttps://en.wikipedia.org/wiki/Monty Hall problemMonty Hall problem ("Ziegenproblem")Suppose you're on a game show, and you're given the choice of three doors:Behind one door is a car; behind the others, goats. You pick a door, say No. 1,and the host, who knows what's behind the doors, opens another door, sayNo. 3, which has a goat. He then says to you, "Do you want to pick doorNo. 2?" Is it to your advantage to switch your choice?Standard assumptions‣ The host must always open a door that was not picked by
Statistical Methods in Particle Physics WS 2017/18 K. Reygers 1. Basic Concepts Useful Reading Material G. Cowan, Statistical Data Analysis L. Lista, Statistical Methods for Data Analysis in Particle Physics Behnke, Kroeninger, Schott, Schoerner-Sadenius: Data Analysis in High Energy Physics: A Practical Guide to Statistical Methods
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Usually z 1 in elementary particle physics, but not in nuclear physics, heavy ion physics or cosmic rays. methods of particle identification : Measure the bending radius ρin a magnetic field B (p B ): mv2 ρ z·e·v·B ρ p zeB γm0βc z with p: momentum; β v c; γ q 1 1 v2 c2. Physics of Particle Detection .
particle physics to technology. They have extended man's knowl edge of his environment and changed his thinking. Direct impact on technology There are also significant short-term spin-offs from particle physics research. Accelerators and the handling of particle beams The demands of particle physics have driven the mastery of acceler
Oxana Smirnova Lund University 2 Basic concepts Particle Physics I. Basic concepts Particle physics studie s the elementary “building blocks” of matter and interactions between them. Matter consists of particles and fields. Particles interact v
What we will cover (partially following Griffiths) 4 1.Some history of particle physics 2.Particle dynamics and a Standard Model (SM) overview 3.How do particle detectors work? Modern particle physics experiments 4.Relativistic kinematics 5.On symmetries 6.Bound states 7.Feynman rules 8.Quantum electron dynamics, QED
Funding particle physicists in astronomy: the National Science Foundation and the Department of Energy V. Summary and conclusions I. Particle Physics and Astrophysics The cosmos is a laboratory to probe the fundamental laws of physics in unique ways that are complementary to accelerator-based particle physics experiments. Observing the cosmos has
agree with Josef Honerkamp who in his book Statistical Physics notes that statistical physics is much more than statistical mechanics. A similar notion is expressed by James Sethna in his book Entropy, Order Parameters, and Complexity. Indeed statistical physics teaches us how to think about
ACCOUNTING 0452/22 Paper 2 October/November 2017 1 hour 45 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction .
