- 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.
MSc Programme in Statistics
MSc Programme in Mathematics-Economics
MSc Programme in Actuarial Mathematics
- 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
4 hours of lectures and 2 hours of exercises each week for seven weeks
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
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.
- 7,5 ECTS
- Type of 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
Criteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Single subject courses (day)
- Theory exercises
- Course number
- 7,5 ECTS
- Programme level
- Full Degree Master
- Block 2
- 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
- Niels Richard Hansen (14-716c686f763175316b6471766871437064776b316e7831676e)
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