Stochastic Modelling

5 credits

Syllabus, Bachelor's level, 1MS007

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MS007
Education cycle: First cycle
Main field(s) of study and in-depth level: Mathematics G1F, Sociotechnical Systems G1F
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 15 March 2007
Responsible department: Department of Mathematics

Entry requirements

Probability and Statistics

Learning outcomes

In order to pass the course (grade 3) the student should

be able to demonstrate a deeper knowledge of probability theory concerning conditional distributions and expectations;

have a knowledge of Poisson processes and life length models and know how to use these in order to assess risks and errors;

understand how to simulate stochastic outcomes using computers;

understand the basics of modelling using Markov chains in discrete and continuous time;

be able to calculate probabilities and expectations for finite Markov chains using the principle of conditioning with respect to the first jump;

understand the meaning of equilibrium for a Markov chain and know how to calculate stationary distributions in simple cases.

Students belonging to the STS program should in addition

have a knowledge of fundamental models for time series, in particular those based on moving averages (the MA-model) and autoregression (the AR-model), and be able to make covariance calculations for those;

be able to give an account of the basic model in renewal theory;

have encountered examples of stochastic modelling of real world phenomena that are of relevance with respect to the profile of the program.

Students belonging to the bioinformatics program should in addition

be able to give an account of the Wright–Fisher model and its population dynamical consequences with respect to fixation of genes, effects of mutations and inherited genetic similarity;

understand the structure of coalescence trees and be able to calculate expected time to nearest common ancestor;

have a knowledge of Markov chain models of DNA chains, in particular models of nucleotide substitution in evolutionary analyses;

be familiar with methods of linearizing protein chains and DNA sequences.

Student belonging to the Bachelor of science program in mathematics may choose any variant of the course.

Content

Stochastic processes, the Poisson process, life length models. Stochastic simulation. Markov chains in discrete and continuous time. Stationary and asymptotic distribution. Absorption probability, absorption time. Selected examples of applications of stochastic modelling, depending on study programme.

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course. Moreover, compulsory assignments may be given during the course.