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Modulbeschreibung

Stochastik

Lehrveranstaltungen:

TitelTypSWSZeitraum
StochastikVorlesung2Sommersemester
StochastikGruppenübung2Sommersemester

Modulverantwortlich:

Prof. Marko Lindner

Zulassungsvoraussetzungen:

Keine

Empfohlene Vorkenntnisse:

Modulziele / angestrebte Lernergebnisse:

Fachkompetenz

Wissen

Students can explain the main definitions of probability, and they can give basic definitions of modeling elements (random variables, events, dependence, independence assumptions) used in discrete and continuous settings (joint and marginal distributions, density functions). Students can describe characteristic notions such as expected values, variance, standard deviation, and moments. Students can define decision problems and explain algorithms for solving these problems (based on the chain rule or Bayesian networks). Algorithms, or estimators as they are caller, can be analyzed in terms of notions such as bias of an estimator, etc. Student can describe the main ideas of stochastic processes and explain algorithms for solving decision and computation problem for stochastic processes. Students can also explain basic statistical detection and estimation techniques.

Fertigkeiten

Students can apply algorithms for solving decision problems, and they can justify whether approximation techniques are good enough in various application contexts, i.e., students can derive estimators and judge whether they are applicable or reliable.

Personale Kompetenzen

Sozialkompetenz

- Students are able to work together (e.g. on their regular home work) in heterogeneously composed teams (i.e., teams from different study programs and background knowledge)  and to present their results appropriately (e.g. during exercise class).

Selbstständigkeit

- Students are capable of checking their understanding of complex concepts on their own. They can specify open questions precisely and know where to get help in solving them.
- Students can put their knowledge in relation to the contents of other lectures.
- Students have developed sufficient persistence to be able to work for longer periods in a goal-oriented manner on hard problems.

Leistungspunkte Modul:

6 LP

Studienleistung:

Klausur

Arbeitsaufwand in Stunden:

Eigenstudium: 124, Präsenzstudium: 56


Lehrveranstaltung: Stochastik

Dozent:

Christian Seifert

Sprache:

Deutsch & Englisch

Zeitraum:

Sommersemester

Inhalt:

Grundbegriffe der Wahrscheinlichkeitstheorie

  • Wahrscheinlichkeitsdefinitionen, bedingte Wahrscheinlichkeiten
  • Zufallsvariablen, Abhängigkeit und Unabhängigkeit von Wahrscheinlichkeiten
  • Rand- und Verbundwahrscheinlichkeiten
  • Verteilungs- und Dichtefunktion
  • Kenngrößen: Erwartungswert, Varianz, Standardabweichung, Momente

Repräsentationsformen für Verbundwahrscheinlichkeiten

  • Bayessche Netzwerke
  • Semantik, Entscheidungsprobleme, exakte und approximative Algorithmen

Stochastische Prozesse

  • Stationarität und Ergodizität
  • Korrelationen
  • Stochastische Signale
  • Warteschlangen

Detektion & Estimation

  • Detektoren
  • Schätzregeln und -verfahren
  • Hypothesen und Verteilungstests
  • Stochastische Regression

Literatur:

  1. Methoden der statistischen Inferenz, Likelihood und Bayes, Held, L., Spektrum 2008
  2. Stochastik für Informatiker, Dümbgen, L., Springer 2003
  3. Statistik: Der Weg zur Datenanalyse, Fahrmeir, L., Künstler R., Pigeot, I, Tutz, G., Springer 2010
  4. Stochastik, Georgii, H.-O., deGruyter, 2009
  5. Probability and Random Processes, Grimmett, G., Stirzaker, D., Oxford University Press, 2001
  6. Programmieren mit R, Ligges, U., Springer 2008

Leistungspunkte Lehrveranstaltung:

6 LP