250054 VO Probabilistic Models in Biomathematics (2021S)
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An/Abmeldung
Hinweis: Ihr Anmeldezeitpunkt innerhalb der Frist hat keine Auswirkungen auf die Platzvergabe (kein "first come, first served").
Details
Sprache: Englisch
Prüfungstermine
Lehrende
Termine (iCal) - nächster Termin ist mit N markiert
https://zoom.us/j/9173785622?pwd=VnUzSStFUHVvU3c0YlFqNEZhb29ydz09
ID de réunion : 917 378 5622Code secret : mE6M9t
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Montag
01.03.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
08.03.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
15.03.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
22.03.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
12.04.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
19.04.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
26.04.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
03.05.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
10.05.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
17.05.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
31.05.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
07.06.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
14.06.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
21.06.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Montag
28.06.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Information
Ziele, Inhalte und Methode der Lehrveranstaltung
Art der Leistungskontrolle und erlaubte Hilfsmittel
Mindestanforderungen und Beurteilungsmaßstab
Strong undergraduate probability. Some knowledge on the following topics: Stochastic processes, Markov processes (discrete and continuous time), Brownian motion, diffusions. No knowledge of measure theory will be required.Art der Leistungskontrolle und erlaubte Hilfsmittel
Two graded home-works will be assigned during the semester. The final exam will be an oral exam (duration to be determined).
Two graded home-works will be assigned during the semester. The final exam will be an oral exam (duration to be determined).
Prüfungsstoff
Will be distributed by email.
Literatur
Will be distributed by email
Zuordnung im Vorlesungsverzeichnis
MBIV
Letzte Änderung: Fr 12.05.2023 00:21
In this course, I will introduce several of the aforementioned probabilistic models and introduce various technics to analyse them. I will start from the Wright-Fisher diffusion(s) describing the evolution of the genetic composition in large populations. I will show that an efficient way to analyse such models relies on the description of their underlying genealogical structure. More precisely, if several individuals are sampled from an extent population, one can trace backward in time the genealogical lines of those individuals. I will show how coalescent theory (Kingman coalescent, $\Lamda$-coalescents) provides an elegant description of this genealogy, and how it allows to draw predictions on the genetic structure of large populations.
If time permits, I will also show how the previous approaches can be carried through in epidemiogy in order to describe a viral expansion (Feller diffusion) and its underlying genealogical structure of such a population (coalescent point processes).
Along the way, I hope to introduce general probabilistic concepts which will be of independent interest : martingales, duality, exchangeability etc.