Topics in Probability and Statistics
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WMMA03905 
Vaknaam  Topics in Probability and Statistics 
Niveau(s)  master 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Topics in Probability and Statistics  
Leerdoelen  At the end of the course, the student is able to: 1. present basic models in population genetics, such as the WrightFisher Model, the Moran model and their relationship to Kingman Coalescence. 2. apply theory for parameter estimation and hypothesis testing using genetic data. 3. explain and apply theory on extensions of basic genetic models involving recombination, natural selection and population structure and growth. 4. interpret genetic trees for infectious disease pathogens and draw conclusions about past spread of the pathogen from those trees. 

Omschrijving  In this course we study mathematical models for Population Genetics and the statistical analysis of DNA sequence data. We use those models to e.g.\ reconstruct ancestral trees, find estimates for the time since the most recent common ancestor of different individuals or species and the time at which a virus entered the human population. After an introduction of some basic biologic and evolutionary theory underlying the mathematical content of this course, mathematical models in population genetics will be introduced. We start with the socalled WrightFisher model and the Moran model. We deduce how these models relate to coalescence theory, a powerful tool for the reconstruction of evolutionary trees of e.g. different species of mammals or of bacteria and viruses causing epidemics among people. After that we discuss some theory on estimation and hypothesis testing based on genetic data. We then extend the most basic models, such as the WrightFisher model by considering biological processes such as recombination and natural selection as well as the impact of population dynamics, such as population growth. As a concrete example we consider the evolution of pathogens (bacteria and viruses) that spread among humans or animals. We discuss how genetic data can be used to estimate the origin, the rate of spread and emergence of possible mutations of concern during an epidemic or pandemic. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Opdracht (ASM)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE)
(The student needs to obtain a pass score both on the assignment and the written exam. In case of nopass the final score is minimum of score for assignment and written exam. In case of pass, the final score is 20% of score for assignment + 80% of score for written exam) 

Vaksoort  master  
Coördinator  prof. dr. J.P. Trapman  
Docent(en)  prof. dr. J.P. Trapman  
Verplichte literatuur 


Entreevoorwaarden  This course assumes knowledge assumed: Probability Theory (WBMA04605), Stochastic Processes (WBMA04805), Statistics (WBMA00905)  
Opmerkingen  The book by Richard Durrett is available on his website https://services.math.duke.edu/~rtd/Gbook/PM4DNA_0317.pdf  
Opgenomen in 
