Module 24-M-FStat Foundations of Statistics

Faculty

Person responsible for module

Regular cycle (beginning)

Every winter semester

Credit points and duration

7 Credit points

For information on the duration of the modul, refer to the courses of study in which the module is used.

Competencies

Non-official translation of the module descriptions. Only the German version is legally binding.

Students understand basic stochastic concepts as well as the foundations of probability theory and statistics; they acquire competences in modelling and analysis of complex relations using probabilistic structures as the basis for applications in particular in statistics. Moreover application examples provide first insights into the application of statistical analyses and modelling using statistical software. Students work in tutorials to improve their skills in the foundations of mathematics, the usage of probability theory for handling data sets in the context of statistics in particular using statistical software. Moreover in the tutorials also presentation and communication skills are acquired. The final exam demonstrates the acquired knowledge in terms of statistical concepts and their relations in the application of statistical methods.

Content of teaching

I. Foundations

  • exploratory data analysis
  • probability theory
  • random variables
  • probability distributions
  • limit theorems

II. Estimation

  • basics (bias, variance, MSE)
  • (method of moments)
  • maximum likelihood
  • Bayesian inference (in particular MCMC)

III. Uncertainty Quantification

  • confidence intervals
  • credible intervals
  • parametric and nonparametric bootstrap

IV. Hypothesis testing

  • Neyman-Pearson
  • likelihood ratio test
  • chi-squared

Recommended previous knowledge

Necessary requirements

Explanation regarding the elements of the module

Module structure: 1 bPr 1

Courses

Foundations of Statistics
Type lecture
Regular cycle WiSe
Workload5 90 h (60 + 30)
LP 3 [Pr]
Tutorial Foundations of Statistics
Type exercise
Regular cycle WiSe
Workload5 60 h (30 + 30)
LP 2

Examinations

portfolio with final examination
Allocated examiner Teaching staff of the course Foundations of Statistics (lecture)
Weighting 1
Workload 60h
LP2 2

Portfolio of exercises, which are usually set weekly during the course, and final examination (usually 90 min) or oral final examination (usually 30 min). The exercises supplement and deepen the content of the lecture.
Participation in exercise groups (presentation of calculation exercises twice when asked. The organiser may replace some of the exercises by exercises in attendance).
Proof of a sufficient number of correctly solved exercises (usually 50% of the points achievable in the semester for solving the exercises).
The final examination relates to the content of the lecture and the tutorial and is used for assessment.

The module is used in these degree programmes:

Degree programme Profile Recom­mended start 3 Duration Manda­tory option 4
Data Science / Master of Science [FsB vom 06.04.2018 mit Änderungen vom 01.07.2019, 02.03.2020, 21.03.2023 und 10.12.2024] Variante 1 1. one semester Obli­gation
Data Science / Master of Science [FsB vom 06.04.2018 mit Änderungen vom 01.07.2019, 02.03.2020, 21.03.2023 und 10.12.2024] Variante 2 1. one semester Obli­gation

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Legend

1
The module structure displays the required number of study requirements and examinations.
2
LP is the short form for credit points.
3
The figures in this column are the specialist semesters in which it is recommended to start the module. Depending on the individual study schedule, entirely different courses of study are possible and advisable.
4
Explanations on mandatory option: "Obligation" means: This module is mandatory for the course of the studies; "Optional obligation" means: This module belongs to a number of modules available for selection under certain circumstances. This is more precisely regulated by the "Subject-related regulations" (see navigation).
5
Workload (contact time + self-study)
SoSe
Summer semester
WiSe
Winter semester
SL
Study requirement
Pr
Examination
bPr
Number of examinations with grades
uPr
Number of examinations without grades
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