Statistics, Data Analysis, and Simulation SS 2017

Transcription

1 Statistics, Data Analysis, and Simulation SS Statistik, Datenanalyse und Simulation Dr. Michael O. Distler Mainz, 20. April 2017

2 The Mainz Microtron 1.6 GeV cw electron beam 100 µa unpolarised beam 30 µa 80 % polarization Energy stability δe/e = 10 6 > 5500 h/yr available for experiments

3 The 3 spectrometer facility Dr. Michael O. Distler <distler@uni-mainz.de> Statistics, Data Analysis, and Simulation SS 2017

4 Learning goals and objectives Students will gain a basic knowledge of statistics, simulation techniques, and numerical methods (algorithms) Problem: determine meaningful and significant information from experimental (empirical) data efficient (economic) data analysis Application of this knowledge in the data analysis Probability of events Uncertainty of a measured quantity Significance of a measurement (discovery) Decision rules for (testing of) model hypotheses Determine (estimate) the best values of parameters Simulation of complex processes Unfolding, factor analysis, pattern recognition,...

5 Contents Introductory Remarks Statistic: probability, distributions, discrete distributions, special continuous distributions, theorems, sampling, multidimensional distributions Monte Carlo methods: random number generators, Monte Carlo integration Parameter estimation: the method of maximum likelihood, variance of the estimators The method of least squares: linear least squares, properties, generalized least squares Hypothesis testing Advanced topics: unfolding, factor analysis, pattern recognition, Bayesian statistics,...

6 Literature V. Blobel, E. Lohrmann: Statistische und numerische Methoden der Datenanalyse, Teubner Verlag (1998), available as blobel/ebuch.pdf S. Brandt: Datenanalyse, BI Wissenschaftsverlag (1999) Philip R. Bevington: Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill (1969) R.J. Barlow: Statistics, John Wiley & Sons (1993) G. Cowan: Statistical Data Analysis, Oxford University Press (1998) W.T. Eadie et al.: Statistical Methods in Experimental Physics, North Holland Publishing Company

7 Administration Home page: Vorlesungen/SS17/Statistik/ Lecture time: Monday, 12:15-13:00, Thursday, 8:15-10:00. and place: seminar room 1, Institut für Kernphysik Problem solving time: Monday, 13:15-14:00 and place: seminar room 1, Institut für Kernphysik Studienleistung : regular and active participation in the practical exercises, solve all 10 problem sets, achieve > 50% total score. Prüfungsleistung : oral examination (30 min) e.g. Vertiefungsvorlesung (Master), benoteter Schein none e.g. Spezialvorlesung (Master), unbenoteter Schein (Diplom)

8 Problem solving classes classical problem sets (comprehension and calculation) computer based problems (put the theory into practice) problems will be handed out after the Thursday lecture (and will be available online) due date is the following Thursday, 10am. Julian Müller will grade the answers and discuss the solutions during the problem solving classes.

9 Examples

10 Examples

11 Examples

12 Introductory Remarks Data analysis is used in many scientific fields, but the lecture here is aimed at mainly physicists. Therefore, a preliminary remark from this view: Physics is the science of quantifiable observations. The comparison: observations classification scheme takes place quantitatively, i.e. it comes to numbers.

13 Introductory Remarks Data analysis in nuclear and particle physics Observe events of a certain type Measure characteristics of each event Theories predict distributions of these properties up to free parameters Some tasks of data analysis: Estimate (measure) the parameters; Quantify the uncertainty of the parameter estimates; Test the extent to which the predictions of a theory are in agreement with the data. Dr. Michael O. Distler <distler@uni-mainz.de> Statistics, Data Analysis, and Simulation SS 2017

14 Introductory Remarks Theory: numbers are calculated using a model. Experiment: numbers are derived from observation. This raises the issue of consistency between theory and experiment. What does consistency or agreement mean? Is there a measure of (non-) agreement?

15 Introductory Remarks Philosophy of Science Karl R. Popper (* 28. Juli 1902 in Vienna, Austria; 17. September 1994 in London, England) coined the term critical rationalism. At the heart of his philosophy of science lies the account of the logical asymmetry between verification and falsifiability. Logik der Forschung, Existence of a true value of measured quantities and derived values.

16 Recipe: How to do science? observation (of nature) hypothesis (model) deduction experiment (reproducible) prediction (falsifiable)? Truth? Important philosophical questions: How to gain knowledge? What is truth? What is a scientific theory?