NSCPHD1096 Point processes (Pointproc)

Volume 2014/2015
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.
  • The R package ppstat.
  • Elements of continuous time martingale theory.
  • Change of measure, the likelihood process and statistical inference.
  • Multivariate event time models.
Learning Outcome

Knowledge: 

 

 

  • Aspects of stochastic analysis with a focus on processes with finite local variation.
  • Statistical methods for estimation and model selection.
  • Concrete multivariate models applied to social and neuron network modeling. 
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 in R.
Competences: Ability to

 

 

 

  • build dynamic models of multivariate event times, fit the models to data, simulate from the models and validate the models.


 

5 hours of lectures for 7 weeks
  • Category
  • Hours
  • Course Preparation
  • 70
  • Exam
  • 40
  • Exercises
  • 61
  • Lectures
  • 35
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Continuous assessment
A total of 3 individual assignments. 2 minor theoretical assignments (each with weight 15%) and 1 mixed theoretical and practical assignment (weight 70%).
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.