ST814: Dispersion Models (10 ECTS)

STADS: 25002801

Level
Master's level course approved as PhD course

Teaching period
The course is offered in the spring semester.

Teacher responsible
Email: bentj@stat.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal.

Prerequisites:
None

Academic preconditions:
A good knowledge of probability theory and mathematical statistics, corresponding to MM506 /812: Probability Theory I and ST519/ST807: Mathematical Statistics or similar courses.

Course introduction
Dispersion models are two - parameter distribution families, which are particularly suited for use in the analysis of non- normally distributed data. The course aims at familiarizing participants with the theory of dispersion models, especially exponential and proper dispersion models, their structure, construction, and their probabilistic and statistical properties.

Qualifications
Participants will gain insight into the mathematical structure of dispersion models, including experience in recognizing dispersion models for a given two - parameter distribution family. Participants will develop skills in manipulating various mathematical elements of dispersion models, in order to

• recognize the different types of dispersion models and describe their similarities and differences;
• be able to manipulate the mathematical elements of dispersion models such as deviance, variance function, normalizing constant, probability density function and saddlepoint approximation;
• obtain an overview of the most important examples of dispersion models and to derive theoretical properties of the new models from the general theory;
vrecognize the importance of different parametrizations of dispersion models using canonical, mean, dispersion and index parameters, and to use this knowledge in practical and theoretical contexts;
• have an overview of convergence results for variance functions, and use these in both practical and theoretical contexts;
• explain the role of dispersion models in statistical modeling of data.

Expected learning outcome
At the end of the course the students are expected to

• have an overview of the various types of dispersion models and the main examples of these, and to know the most important literature in the field;
• be skilled at manipulating the mathematical elements and different parametrizations of the different types of dispersion models;
• have confidence in the use of the theoretical results for dispersion models on concrete examples and explain the practical interpretation of the results;
• have an understanding of the application of dispersion models in the statistical modeling of data.

Subject overview
Dispersion models and proper dispersion models. Natural exponential families. Variance functions and their use for characterization and convergence. Exponential dispersion models. Quadratic variance functions. Power variance function and Tweedie models. Tweedie convergence theorem. Extreme, geometric, discrete, and other types of dispersion models.

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:

1. Project report, is evaluated by external censorship by the Danish 7-mark scale (10 ECTS). (25002802)

The reexamination can have another form than the ordinary exam.

Expected working hours
The teaching method is based on three phase model.
Intro phase: 60 hours
Skills training phase: 30 hours, hereof:
 - Tutorials: 30 hours

Educational activities Study phase: 30 hours

Language
This course is taught in English, if international students participate. Otherwise the course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.