13863 - Mathematical Statistics Modulübersicht

Module Number: 13863
Module Title:Mathematical Statistics
  Mathematische Statistik
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. Hartmann, Carsten
  • Prof. Dr. rer. nat. habil. Wunderlich, Ralf
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: On special announcement
Credits: 8
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.
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
Recommended Prerequisites:Knowledge of the content of module 
  • 11217: Probability Theory
Mandatory Prerequisites:No successful participation in module 11331 - Mathematische Statistik.
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 150 Hours
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)
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
  • Bachelor (research-oriented) / Informatik / PO 2008 - 1. SÄ 2017
  • Master (research-oriented) / Informatik / PO 2008 - 2. SÄ 2017
  • Bachelor (research-oriented) / Künstliche Intelligenz / PO 2022
  • Bachelor (research-oriented) / Mathematik / PO 2019
  • Master (research-oriented) / Physics / PO 2021
  • Bachelor (research-oriented) / Wirtschaftsmathematik / PO 2019 - SÄ 2021
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  „Advanded Methods“
  • Study programme Artificial Intelligence B.Sc.: Compulsory elective module in complex „Mathematics“
Module Components:
  • Lecture: Mathematical Statistics
  • Accompanying exercise
  • Related examination
Components to be offered in the Current Semester: