Introduction to Data Analysis

The module will give an introduction into the basic techniques for the analysis of experimental data. It will cover among other things the following topics:

• The scientific method
• The concept of probability and its interpretations
• Bayes' theorem
• Random variables
• Probability distributions and their moments
• Important distributions: binomial, multinomial, Poisson and Gaussian distribution
• Multivariate distributions
• Marginal and conditional probability distributions
• Covariance and correlation coefficient
• Functions of (multiple) random variables
• Central limit theorem
• Gaussian uncertainty propagation for n-dimensional functions and covariance matrix
• Statistical and systematic uncertainties
• Parameter estimation using the method of least squares
• Estimating the goodness of fit
• Parameter estimation using the (extended) maximum-likelihood method
• Relation between least-squares and maximum-likelihood method
• Estimating the significance of a signal

After successful completion of this module, students are able to

• understand and apply fundamental statistical concepts
• understand and apply basic data-analysis techniques to suitable data
• apply first-order uncertainty propagation in the most general case
• estimate and correctly interpret statistical and systematic uncertainties
• estimate model parameters by performing fits to (multi-dimensional) data
• estimate the statistical significance of signals in the presence of background
• (when attending the tutorials) develop tools for moderately complex data-analysis tasks using the Python programming language

No preconditions in addition to the requirements for the Master’s program in Physics.

This module consists of a lecture and an excercise course.

The goal of the lecture is to provide a solid theoretical background. To this end, methods and concepts will be derived, where possible, from first principles.

In the tutorials, the concepts that are explained in the lecture will be applied to concrete examples. In small groups of students, short Python programs will be developed. The examples will be mostly from particle physics. However, the tutorials will focus mainly on the statistical aspects of the problems and are prepared such that they do not require deeper particle-physics preknowledge.

Presentation with projector, board work, Smartboard, problem sheets

• G. Cowan: Statistical data analysis, Oxford University Press, (1998)
• R. J. Barlow: Statistics: A Guide to the Use of Statistical Methods in the Physical Sciences, Wiley, (2008)
• S. Brandt: Datenanalyse für Naturwissenschaftler und Ingenieure, Springer Spektrum, (2013)
• B. Roe: Probability and Statistics in Experimental Physics, Springer, (2001)
• M.G. Kendall & A. Stuart: The Advanced Theory of Statistics Vol I-III, Charles Griffin, (1961)
• V. Blobel & E. Lohrmann: Statistische und numerische Methoden der Datenanalyse, Teubner Studienbücher Verlag, (1998) 
• D.S. Sivia & J. Skilling: Data Analysis: a Bayesian Tutorial, Oxford University Press, (2006)
• P.R. Bevington & D.K. Robinson: Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, (2002)
• L. Lyons: Statistics for Nuclear and Particle Physicists, Cambridge University Press, (1989)

There will be an oral exam of 30 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions.

For example an assignment in the exam might be:

• What is the mathematical definition of probability?
• What is the method of least squares?
• What is the method of maximum likelihood estimation?

Participation in the exercise classes is strongly recommended since the exercises prepare for the problems of the exam and rehearse the specific competencies.