Kursussøgning, efter- og videreuddannelse – Københavns Universitet

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Kursussøgning, efter- og videreuddannelse

Statistical inferens for Markov processes

Practical information
Study year 2016/2017
Time
Block 1
Programme level Ph.D.
ECTS 7,5 ECTS
Course responsible
  • Mogens Bladt (5-4b756a6d7d49766a7d7137747e376d74)
  • Department of Mathematical Sciences
Course number: NSCPHD1076

Course content

 

PLEASE NOTE         

The PhD course database is under construction. If you want to sign up for this course, please click on the link in order to be re-directed. Link: https://phdcourses.ku.dk/nat.aspx

 

The course will focus on statistical inferens and estimation of Markov processes. We will consider the following processes: Markov chains, fully observed Markov jump process, discretely observed Markov jump processes and discretely observed diffusions. While the estimation in the fully observed models is relatively easy and linked to methods for multinomial distributions, the estimation of the discretely observed processes is more involved. Here we shall make use of incomplete data methods like the EM algortihm and Markov chain Monte Carlo methods. Markovian bridges play an important role and both explicit methods and simulation will be exploited. The explicit methods calculates conditional expectations of sufficient statistics using Markov chain theory.

The methods will be applied to financial data from credit risk modeling (discretely observed Markov jump processes), stock prices (discretely observed diffusions) and ruin probability estimation (insurance risk) using estimation of phase--type distributions and Markov chain Monte Carlo.          

Necessary background on Markov processes and incomplete data methods will be provided as an integrated part of the course.  

 

 

 

 

Learning outcome

At the end of the course the student is expected to have:

Knowledge about inference for Markov processes, fully or discretely observed, Markov bridges and incomplete data methods in the context.

Skills: At the end of the course the student is expected to be able to 
follow and reproduce arguments at a high abstract level corresponding to 
the contents of the course. 

Competences in the contents of the course.

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Education

PhD programme in Actuarial Mathematics
PhD programme in Statistics
PhD programme in Probabilty Theory

 

Studyboard

Natural Sciences PhD Committee

Course type

Single subject courses (day)

Duration

1 block

Schedulegroup

C
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Teaching and learning methods

7 weeks with 4 lectures.

Capacity

No restrictions/ no limitations

Language

English

Workload

Category Hours
Preparation 178
Lectures 28
English 206

Exam

Type of assessment

Oral examination, 30 min
30 min preparation

Aid

All aids allowed

Marking scale

passed/not passed

Criteria for exam assessment

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

Censorship form

No external censorship

Re-exam

Same as ordinary.

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