Inference for Stochastic Differential Equations
Stochastic processes given as solutions to stochastic differential equations are popular models in physics, biology, finance, social sciences and many other fields. In this course, we study concepts and theory behind stochastic differential equations and methods for doing statistical inference.
MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics-Economics
MSc Programme in Statistics
- definition and interpretation of stochastic differential equation models.
- probabilistic properties of stochastic differential equation models.
- simulation algorithms and R-packages for stochastic differential equation models.
- statistical methods for parameter estimation in stochastic differential equation models.
Skills: Ability to
- perform a statistical analysis of data from stochastic differential equation models.
- compute parameter estimates and construct confidence intervals for these models.
- perform model diagnostics, statistical tests, model selection and model assessment for these models.
- use R to be able to work with the above points for practical data analysis.
Competences: Ability to
- construct stochastic differential equation models.
- do statistical inference and simulate trajectories from these models.
- evaluate if a given model is adequate.
4 hours of lectures for 7 weeks.
4 hours of exercises for 7 weeks, of which 2 hours are for practical work.
See Absalon for a list of course literature.
Basic knowledge of probability theory (such as densities,
conditional independence, conditional distributions and the Markov
property) and standard statistical tools (such as likelihood
theory, regression techniques and tests); e.g., it suffices to have
passed StatMet and MStat, Sand and Statistics A (or courses that
are equivalent to these courses; Statistics A can be replaced by
Basic knowledge of programming in R.
The mandatory group project will have mandatory feedback by other students in the course.
- 7,5 ECTS
- Type of assessment
Continuous assessment under invigilation
- Type of assessment details
- The continuous assessment is composed of three elements that
are to be completed during the course.
The three elements consist of an overall evaluation of 2 out of 3 individual quizzes and a group assignment.
The quizzes will be of one hour each, which will be taken as part of the teaching and under surveillance in block weeks 4, 6 and 8.
The group assignment should be handed in twice.
The first time it will be handed in for peer-review by other students.
The assignment will be handed in a second time after taking the feedback into account. The final evaluation of the assignment is exclusively based on the second hand-in.
In the group assignment the contributions from each student have to be clearly stated.
Each quiz as well as the group assignment will be evaluated and assigned points between 0 and 100. Each element is passed if it obtains at least 50 out of 100 points.
Each of the three elements must be passed separately to pass the course.
For the final grade the two best results from the quizzes will each count 25% in the final grade and the group assignment will count 50% in the final grade.
If the group assignment is passed, it is valid for the reexam the same year and the ordinary exam the year after.
- All aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal censor
Criteria for exam assessment
The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.
Single subject courses (day)
- Theory exercises
- Project work
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 2
- No limit.
The number of seats may be reduced in the late registration period.
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Susanne Ditlevsen (7-7d7f7d6b78786f4a776b7e7238757f386e75)
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Courseinformation of students