ST813: Statistical Modelling

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N370004102
Censorship: Second examiner: External
Grading: 7-point grading scale
Offered in: Odense
Offered in: Spring
Level: Master's level course approved as PhD course

STADS ID (UVA): N370004101
ECTS value: 10

Date of Approval: 26-10-2018


Duration: 1 semester

Version: Approved - active

Comment

25002701(former UVA) is identical with this course description. 
The course cannot be chosen by students who have passed the course ST523

Entry requirements

None

Academic preconditions

Students taking the course are expected to:

  • Have knowledge of linear algebra, calculus, basic statistics
  • Be able to use the statistical software R 

Course introduction

The aim of the course is to enable the student to gain insight into the
mathematical structure of linear and generalized linear models,
including experience in recognizing such models from a given statistical
problem.

The course builds on the knowledge acquired in the courses
ST521: Mathematical Statistics and on knowledge of linear algebra
corresponding to the course MM538: Algebra and Linear Algebra, and gives
an academic basis for advanced courses in statistics and master thesis
projects.

In relation to the competence profile of the degree it is the explicit focus of the course to:

  • have
    an overview of the various types of linear and generalized linear
    models and the main examples of these, as well as to identify which
    problems can be solved by means of such models;
  • be skilled at
    manipulating the mathematical and statistical elements of linear and
    generalized linear models and to clearly distinguish between exact and
    asymptotic results;
  • know how to securely apply the theoretical
    results for linear and generalized linear models to concrete examples
    and explain the practical interpretation of the results
  • have familiarity with the statistical package R, and routine in its use for statistical modeling.

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

  • recognize
    the different types of statistical models and describe their
    similarities and differences, and explain the role that the response
    variable, explanatory variables, variance function and link function
    play for statistical modeling;
  • be able to manipulate the
    mathematical and statistical elements of linear and generalized linear
    models, such as parameters and principles of estimation, the derivation
    of statistical tests based on standard errors deviance and residual sum
    of squares;
  • obtain an overview of the most important examples of
    linear and generalized linear models, and to derive theoretical
    properties of new models based on the general theory;
  • recognize
    the importance of and the difference between regression and dispersion
    parameters, and use this knowledge in practical and theoretical
    contexts:
  • carry out practical data analysis using statistical
    modeling, including investigation of a model’s adequacy using residual
    analysis;
  • perform the statistical analysis using the statistical
    software R, including the ability to identify and interpret relevant
    information in the program output;
  • document the results of a statistical analysis in the form of a written report.

Content

The following main topics are contained in the course:
  • Linear models, simple and multiple regression. 
  • Parameter estimation, hypothesis tests and confidence regions. 
  • Residual analysis. 
  • Transformation of variables, polynomial regression. 
  • The one-way ANOVA model. 
  • Model building and variable selection. 
  • Prediction.
  • Natural exponential families; moment generating functions; variance functions; 
  • Dispersion models; 
  • Likelihood theory; 
  • Chi -square, F- and t-tests; analysis of deviance; 
  • Iterative least- squares algorithm; 
  • Normal-theory linear models, 
  • Logistic regression, 
  • Analysis of count data, positive data.

Literature

See Blackboard for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

Spring

Tests

2 take-home assignments, graded overall

EKA

N370004102

Censorship

Second examiner: External

Grading

7-point grading scale

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

10

Additional information

The examination form for re-examination may be different from the exam form at the regular exam.

Indicative number of lessons

80 hours per semester

Teaching Method

In the intro phase a modified version of the classical lecture is employed, where the terms and concepts of the topic are presented, from theory as well as from examples based on actual data. In these hours there is room for questions and discussions. In the training phase the students work with data-based problems and discussion topics, related to the content of the previous lectures in the intro phase. In these hours there is a possibility of working specifically with selected difficult concepts. In the study phase the students work independently with problems and the understanding of the terms and concepts of the topic. Questions from the study phase can afterwards be presented in either the intro phase hours or the training phase hours.

Educational activities 

The students are expected to:

  • Work with the new concepts and terms introduced.
  • Increase their understanding of the topics covered during the lectures.
  • Solve relevant exercises.
  • Read the text book chapters and the scientific journal articles provided as support for the lectures

Teacher responsible

Name E-mail Department
Fernando Colchero colchero@imada.sdu.dk

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration & Legality

NAT

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