NMAK22008U Point Processes
Volume 2022/2023
Education
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
MSc Programme in Actuarial Mathematics
Content
- Random measures and Poisson processes.
- Stochastic processes with locally bounded variation.
- Integration w.r.t. random measures and locally bounded variation processes.
- Stochastic integral equations, numerical solutions and simulation algorithms.
- Elements of continuous time martingale theory.
- Change of measure, the likelihood process and statistical inference.
- Multivariate asynchronous event time models.
Learning Outcome
Knowledge:
- Aspects of stochastic analysis for processes with finite local variation.
- Statistical methods for estimation and model selection.
- Applications of concrete multivariate recurrent event time models.
Skills: Ability to
- compute with stochastic integrals w.r.t. locally bounded variation processes
- construct univariate and multivariate models as solutions to stochastic integral equations
- simulate solutions to stochastic integral equations
- estimate parameters via likelihood and penalized likelihood methods
- implement the necessary computations
- build dynamic models of multivariate event times, fit the models to data, simulate from the models and validate the models.
Competences: Ability to
- analyze mathematical models of events with appropriate probabilistic techniques
- develop statistical tools based on the mathematical theory of event times
- assess which asynchronous event time models are appropriate for a particular data modelling task
Recommended Academic Qualifications
Probability theory and
mathematical statistics on a measure theoretic level. Knowledge of
stochastic process theory including discrete time martingales and
preferably aspects of continuous time stochastic processes.
The courses StatMet and MStat (alternatively MatStat from previous years), Regression and Advanced Probability 1+2 are sufficient. Advanced Probability 2 can be followed at the same time.
The courses StatMet and MStat (alternatively MatStat from previous years), Regression and Advanced Probability 1+2 are sufficient. Advanced Probability 2 can be followed at the same time.
Teaching and learning methods
4 hours of lectures and 2
hours of exercises each week for seven weeks
Workload
- Category
- Hours
- Lectures
- 28
- Preparation
- 104
- Theory exercises
- 14
- Exam
- 60
- Total
- 206
Feedback form
Oral
Individual
Continuous feedback during the course
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Exam
- Credit
- 7,5 ECTS
- Type of assessment
- Continuous assessment
- Type of assessment details
- A total of 3 individual assignments. 2 minor theoretical assignments (each with weight 15%) and 1 mixed theoretical and practical assignment (weight 70%).
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
one internal examiner
- Re-exam
Same as ordinary. Each of three assignments from the ordinary exam can be reused or remade.
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
- NMAK22008U
- Credit
- 7,5 ECTS
- Level
- Full Degree Master
- Duration
- 1 block
- Placement
- Block 2
- Schedule
- A
- Course capacity
- The number of seats may be reduced in the late registration period
Study board
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinators
- Niels Richard Hansen (14-78736f767d387c38726b787d6f784a776b7e7238757f386e75)
Saved on the
07-04-2022