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250054 VO Probabilistic Models in Biomathematics (2021S)
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Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).
Details
Language: English
Examination dates
Lecturers
Classes (iCal) - next class is marked with N
https://zoom.us/j/9173785622?pwd=VnUzSStFUHVvU3c0YlFqNEZhb29ydz09
ID de réunion : 917 378 5622Code secret : mE6M9t
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Monday
01.03.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
08.03.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
15.03.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
22.03.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
12.04.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
19.04.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
26.04.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
03.05.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
10.05.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
17.05.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
31.05.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
07.06.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
14.06.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
21.06.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock -
Monday
28.06.
15:00 - 17:15
Digital
Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
Information
Aims, contents and method of the course
Assessment and permitted materials
Minimum requirements and assessment criteria
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).
Examination topics
Will be distributed by email.
Reading list
Will be distributed by email
Association in the course directory
MBIV
Last modified: 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.