ST816: Computational Statistics

The Study Board for Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N370022102
Assessment: 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): N370022101
ECTS value: 10

Date of Approval: 05-10-2022


Duration: 1 semester

Version: Approved - active

Comment

The course is co-read with ST522.

Entry requirements

Students who have passed ST522 cannot follow the course.

Academic preconditions

Students taking the course are expected to have knowledge of mathematical statistics (at the level of ST521 Mathematical Statistics or equivalent).

Course introduction

The aim of the course is to enable the student to use modern computer intensive statistical methods as tools to investigate stochastic phenomena and statistical procedures, and to perform statistical inference, which is important in regard to conducting statistical analysis based on computation and simulation.

The course builds on the knowledge acquired in the courses calculus and mathematical statistics, and gives an academic basis for studying the topics probability theory, order statistics and extreme value statistics, that are part of the degree.

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give the competence to handle model building and/or model calculations.
  • Give skills to perform statistical analyses.
  • Give theoretical knowledge about and practical experience with the application of methods and models in statistics.

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:
  • Reproduce key theoretical results concerning elementary operations on random variables and vectors, and to apply these to simple theoretical assignments.
  • Reproduce and apply the fundamental theorems of random variate generation.
  • Simulate variates and vectors from the most common distributions.
  • Evaluate the quality of a random number generator.
  • Apply the basic principles of variance reduction.
  • Simulate complex systems and investigate their properties.
  • Use simulation to approximate integrals.
  • Use simulation to compute p-values and confidence intervals.
  • Investigate properties of statistical procedures and estimators using simulation.
  • Perform programming relevant to the content of the course in the statistical package used in the course.
  • Identify and interpret relevant information in the output of the statistical package used in the course.
  • Summarize the results of an analysis in a statistical report.

Content

The following main topics are contained in the course:
Random number generators, inversion method, rejection sampling, simulation from multivariate distributions, Markov Chain Monte Carlo methods, permutation and randomization tests, transformations, simulation of experiments and complex systems, Monte Carlo integration, simulation of stochastic processes, bootstrap methods, Bayesian models and methods, EM algorithm, nonparametric density estimation.

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

June

Tests

Portfolio consisting of projects and oral exam

EKA

N370022102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Full name and SDU username

Language

Normally, the same as teaching language

Duration

60 minutes (30 minutes preparation time and 30 minutes actual oral exam)

Examination aids

To be announced during the course

ECTS value

10

Indicative number of lessons

92 hours per semester

Teaching Method

The teaching activities are reflected in an estimated allocation of the workload of an average student as follows:

  • Intro phase (lectures) - 56 hours
  • Training phase: 36 hours, including 10 hours tutorials and 26 hours laboratory

Educational activities: Studying the course material and preparing the weekly exercises, individually or through group work.

Teacher responsible

Name E-mail Department
Vaidotas Characiejus characiejus@imada.sdu.dk Analysis

Additional teachers

Name E-mail Department City
Hans Chr. Petersen hcpetersen@sdu.dk Data Science

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.