NMAK14024U Stochastic models for genetic data
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
Introduction to topics in Statistical Genetics, that is, the development and application of statistical methods for drawing inferences from genetic data. The course will develope mathematical theory and statistical models to understand how genetic data vary in a population. The theory and models are based on Markov processes, in discrete and continuous time.
The biological focus is on understanding how individuals are related genetically in a population (human, animal, plant populations) and how we statistically understand genetic variation. Key mathematical/statistical concepts are ancestral processes (particular Markov processes), the coalescent, the age and frequency of alleles (genetic types) in populations, and inference for genetic data using such processes. Relatedness is desribed in terms of a graph.
During the course the student will do a small project of theoretical or practical nature.
Knowledge
At the end of the course the student will have knowledge about how
genetic variation is modelled, ancestral processes, and how
inference can be made from such processes. The student will have
the knowledge to
- explain population genetic models, like the Wright-Fisher model
- explain the coalescent process and Ewens sampling formula
- explain the frequency distribution of alleles (types)
- explain statistical methods for inference on genetic data
- explain what a genealogy is
- explain the use of Markov chains to model genetic variation
Skills
The student will acquire the skills to analysis simple genetic data
sets, and to extract basic mathematical properties about ancestral
processes.
Competencies
At the end of the course the students will have the competence
to
- carry out inference for (simple) genetic data sets
- extract relevant mathematical properties of genetic models
- extract biological insight from mathematical/statistical models
Tavare, S (2004). Ancestral inference in population genetics.
In: Lectures on Probability Theory and Statistics. Saint-Flour XXXI
– 2001. (Ed. Picard J.). Lecture Notes in Mathematics, 1837, 1–188,
2004. Springer Verlag, New York.
These notes can be obtained in pdf from Simon Tavare’s home page
(look under 2004):
http://www.cmb.usc.edu/people/stavare/allstpapers.html
- Category
- Hours
- Exam
- 45
- Exercises
- 21
- Lectures
- 28
- Preparation
- 112
- Total
- 206
As
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- Credit
- 7,5 ECTS
- Type of assessment
- Written examination, 4 hours under invigilation---
- Exam registration requirements
- Approved oral presentation of project during the course
- Aid
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
- Re-exam
- Oral exam; 30 min without preparation; requires approved project, same as for ordinary exam
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Course information
- Language
- English
- Course code
- NMAK14024U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 3
- Schedule
- A (Tues 8-12 + Thurs 8-17)
- Course capacity
- No limit
- Continuing and further education
- Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Course responsibles
- Carsten Wiuf (4-7c6e7a6b457266796d33707a336970)
Lecturers
Carsten Wiuf