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# Computerbased Data Analysis

## Module PH2099

This module handbook serves to describe contents, learning outcome, methods and examination type as well as linking to current dates for courses and module examination in the respective sections.

### Module version of WS 2016/7

There are historic module descriptions of this module. A module description is valid until replaced by a newer one.

Whether the module’s courses are offered during a specific semester is listed in the section Courses, Learning and Teaching Methods and Literature below.

available module versions
SS 2020SS 2019SS 2018WS 2016/7WS 2010/1

### Basic Information

PH2099 is a semester module in German or English language at Master’s level which is offered in winter semester.

This module description is valid from WS 2016/7 to WS 2019/20.

If not stated otherwise for export to a non-physics program the student workload is given in the following table.

150 h 70 h 5 CP

Responsible coordinator of the module PH2099 in the version of WS 2016/7 was Boris Grube.

### Content, Learning Outcome and Preconditions

#### Content

The lecture 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

#### Learning Outcome

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 C++ framework "ROOT"

#### Preconditions

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

### Courses, Learning and Teaching Methods and Literature

#### Learning and Teaching Methods

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 C++ programs will be developed using the C++ data analysis framework "ROOT". 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.

#### Media

Presentation with projector, board work, Smartboard, problem sheets

#### Literature

• G. Cowan, "Statistical data analysis", Oxford University Press.
• R. J. Barlow, "Statistics: A guide to the use of statistical methods in the Physical Sciences", Wiley Verlag.
• S. Brandt, "Datenanalyse für Naturwissenschaftler und Ingenieure", Springer Spektrum.
• B. Roe, "Probability and Statistics in Experimental Physics", Springer Verlag.
• M. G. Kendall and A. Stuart, "The Advanced Theory of Statistics Vol I-III", Charles Griffin, London.
• V. Blobel und E. Lohrmann, "Statistische und numerische Methoden der Datenanalyse", Teubner Studienbücher Verlag.
• D. S. Sivia and J. Skilling, "Data Analysis, a Bayesian Tutorial", Oxford Science Publications.
• P. R. Bevington and D. K. Robinson, "Data reduction and error analysis for the physical sciences", McGraw-Hill.
• L. Lyons, "Statistics for nuclear and particle physics", Cambridge University Press.

### Module Exam

#### Description of exams and course work

In a written exam of 60 minutes the learning outcome is tested using comprehension questions and sample problems.

In accordance with §12 (8) APSO the exam can be done as an oral exam. In this case the time duration is 25 minutes.

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