NMAK14024U Stochastic models for genetic data

Volume 2014/2015
Education
MSc Programme in Mathematics
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
Content

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.

Learning Outcome

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

VidSand1, Stat1, Beting
4 hours of lecturing, 3 hours of exercise classes per week for 7 weeks.
  • Category
  • Hours
  • Exam
  • 45
  • Exercises
  • 21
  • Lectures
  • 28
  • Preparation
  • 112
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Written examination, 4 hours under invigilation
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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.