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Statistics Lab

General

study semester
2
standard study semester
6
cycle
jedes Sommersemester
duration
1 Semester
SWS
4
ECTS
6
teaching language
Deutsch oder Englisch

People

responsible
Prof. Dr. Verena Wolf
Prof. Dr. Vera Demberg
lectures
Prof. Dr. Verena Wolf
Prof. Dr. Vera Demberg

Assessment & Grades

entrance requirements
none
assessment / exams

mündliche oder schriftliche Prüfung

grade

Wird aus Leistungen in der Klausur, sowie den Prüfungsvorleistungen ermittelt. Die genauen Modalitäten werden vom Modulverantwortlichen bekannt gegeben. Alle Modulelemente sind innerhalb eines Prüfungszeitraumes erfolgreich zu absolvieren.

Workload

course type /weekly hours
  2 SWS Vorlesung
+ 2 SWS Übung
= 4 SWS
total workload
   60 h Präsenzstudium
+ 120 h Eigenstudum
= 180 h (= 6 ECTS)

Aims / Competences to be developed

  • Verständnis der mathematischen Konzepte von Zufallsvariablen und Verteilungen
  • Verständnis und Anwendung von Methoden der Punkt-und Intervalschätzung, statistischer Tests
  • Verständnis der mathematischen Konzepte von zustandsdiskreten Markovprozessen und Verwendung solcher Prozesse zur Beschreibung von realen Phänomenen

Content

Probabilities and Discrete Random Variables

  • Probability
  • discrete RVs
  • expectation, variance and quantiles (also visualization of them)
  • higher moments
  • important discrete probability distributions
  • Generating discrete random variates Continuous Random Variables and Laws of Large Numbers
  • σ-algebras (very lightweight)
  • Continuous Random Variables
  • Important Continuous Distributions
  • generating continuous random variates
  • Chebyshev’s inequality
  • Weak/Strong Law of Large Numbers
  • Central Limit Theorem

Multidimensional Probability Distributions

  • joint probability distribution
  • conditional probability distribution
  • Bayes' Theorem
  • covariance and correlation
  • independence
  • important multidimensional probability distributions

Point Estimation

  • (generalized) method of moments
  • maximum likelihood estimation
  • Bayesian inference (posterior mean/median, MAP)
  • Kernel density estimation
  • OLS estimator (this is simple regression but should be mentioned here!)
  • (shortly: model selection)

Interval Estimation

  • confidence intervals for sample mean/variance
  • confidence intervals for MLE
  • bootstrap confidence interval
  • Bayesian credible interval

Statistical Testing

  • Level α tests (Z-Test, T-Test)
  • p-value
  • chi-squared tests, Fisher test
  • multiple testing (Bonferroni correction, Holm-Bonferroni method, Benjamini-Hochberg, etc)

Discrete-time Markov chains (only if time)

  • transient distributions
  • equilibrium distributions
  • Monte-Carlo simulation

HMMs

  • Baum-Welch-Algorithmus
  • Viterbi-Algorithmus

Literature & Reading

Additional Information

Curriculum

This module is part of the following study programmes:

Cybersicherheit BSc: Grundlagen der Informatik
study semester: 2 / standard study semester: 6
Medieninformatik BSc: Grundlagen der Informatik
study semester: 4 / standard study semester: 6
Data Science and Artificial Intelligence BSc: Spezialisierter Bereich DSAI
study semester: 2 / standard study semester: 6
Cybersecurity BSc (English): Grundlagen der Informatik
study semester: 4 / standard study semester: 6