# NMAK23005U Inference for Stochastic Differential Equations

Volume 2023/2024
Education

MSc Programme in Actuarial Mathematics
MSc Programme in Mathematics-Economics
MSc Programme in Statistics

Content

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.

Learning Outcome

Knowledge:

• 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.

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 ModComp).
Basic knowledge of programming in R.
4 hours of lectures for 7 weeks.
4 hours of exercises for 7 weeks, of which 2 hours are for practical work.
• Category
• Hours
• Lectures
• 28
• Preparation
• 97
• Theory exercises
• 28
• Project work
• 50
• Exam
• 3
• Total
• 206
Oral
Collective
Continuous feedback during the course of the semester
Peer feedback (Students give each other feedback)

The mandatory group project will have mandatory feedback by other students in the course.

Credit
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.
Aid
All aids allowed
Marking scale