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Module Number:
| 13863
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| Module Title: | Mathematical Statistics |
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Mathematische Statistik
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| Department: |
Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
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| Responsible Staff Member: | -
Prof. Dr. rer. nat. Hartmann, Carsten
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Prof. Dr. rer. nat. habil. Wunderlich, Ralf
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| Language of Teaching / Examination: | English |
| Duration: | 1 semester |
| Frequency of Offer: |
On special announcement
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| Credits: |
8
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| Learning Outcome: | The students
- are skilled in probability theory,
- know the basic statistical models and learn how to correctly use statistical methods
- can study advanced topics in stochastics
- understand statistical methods thoroughly to avoid biased and false conclusions
- are experienced in autonomously doing research based on specific applications.
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| Contents: | - Descriptive statistics (central tendency and variation, quantiles, linear regression)
- Parameter estimation (point estimates, confidence intervals, Bayesian estimastion, sufficient statistic)
- Hypothesis testing (statistical tests, Neyman-Pearsonlemma, one- and two-sided tests)
- Linear models (regression and variance analysis, linear classification, Gauss-Markov theorem)
- Applications and use of statistical software
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| Recommended Prerequisites: | Knowledge of the content of module
- 11217: Probability Theory
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| Mandatory Prerequisites: | No successful participation in module 11331 - Mathematische Statistik. |
| Forms of Teaching and Proportion: | -
Lecture
/ 4 Hours per Week per Semester
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Exercise
/ 2 Hours per Week per Semester
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Self organised studies
/ 150 Hours
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| Teaching Materials and Literature: | - G. Casella, R.L. Berger. Statistical Inference. Duxbury, 2002
- W.R. Pestman. Mathematical Statistics. De Gruyter 1998
- Jun Shao, Mathematical Statistics, Springer, 2003, DOI: 10.1007/b97553
- H.-O. Georgii, Stochastics: Introduction to Probability and Statistics, De Gruyter, 2008 (DOI: 10.1515/9783110206760)
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| Module Examination: | Prerequisite + Final Module Examination (MAP) |
| Assessment Mode for Module Examination: | Prerequisite:
- Successful completion of homework
Final module examination:
- Written examination, 90 min. OR
- Oral examination, 30 min.
In the first lecture it will introduced, if the examination will organized in written or oral form. |
| Evaluation of Module Examination: | Performance Verification – graded |
| Limited Number of Participants: | None |
| Part of the Study Programme: | -
Master (research-oriented) /
Artificial Intelligence /
PO 2022
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Bachelor (research-oriented) /
Informatik /
PO 2008
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Master (research-oriented) /
Informatik /
PO 2008
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Bachelor (research-oriented) /
Mathematik /
PO 2019
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Bachelor (research-oriented) /
Mathematik /
PO 2023
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Bachelor (research-oriented) - Co-Op Programme with Practical Placement /
Mathematik - dual /
PO 2023
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Master (research-oriented) /
Physics /
PO 2021
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| Remarks: | - Study programme Mathematics B.Sc.: Compulsory elective module in complex „Specialisation“
- Study programme Economathematics B.Sc.: Compulsory elective module in complex „Specialisation“
- Study programme Physics M.Sc.: Compulsory elective module in complex „Minor Subject“
- Study programme Computer Science B.Sc.: Compulsory elective module in „Applied Mathematics“ or in field of application „Mathematics“
- Study programme Computer Science M.Sc.: Compulsory elective module in „Mathematics“ or in field of application „Mathematics“
- Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex „Advanced Methods“
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| Module Components: | - Lecture: Mathematical Statistics
- Accompanying exercise
- Related examination
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| Components to be offered in the Current Semester: | |
