Syllabus:

# Computer Intensive Methods in Statistics, 7.5 Credits

Swedish name: Datorintensiva statistiska metoder

This syllabus is valid: 2018-01-15 and until further notice

Course code: 5MS063

Credit points: 7.5

Education level: Second cycle

Main Field of Study and progress level: Mathematical Statistics: Second cycle, has only first-cycle course/s as entry requirements
Statistics: Second cycle, has only first-cycle course/s as entry requirements

Established by: Faculty Board of Science and Technology, 2018-03-19

## Contents

Element 1 (5.0 credits): Theory. The element covers the theory of simulation and computer intensive statistical methods, i.e. techniques for attacking problems that are hard to solve analytically. In the element, generating random numbers from different distributions, integral estimation with error estimation, methods for variance reduction such as using antithetic variables and control variables, conditioning, and importance- and stratified sampling, are treated. Furthermore, simulating Poisson processes and queuing systems are covered. Finally, methods for constructing confidence intervals and conducting tests of hypotheses, using non-parametric and parametric bootstrap, for one- and multidimensional data, are treated.

Element 2 (2.5 credits): Computer labs. The element includes application of computer intensive statistical methods with suitable software.

## Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding
• thoroughly account for the most important methods for generating random numbers from the most common discrete and continuous probability distributions
Skills and abilities
• independently apply the methods for generating random numbers from the most common discrete and continuous probability distributions
• apply bootstrap methods in order to construct confidence intervals and test hypotheses
• critically apply the most common methods for variance reduction, and make error estimations for them
• present results from simulation studies in written form
Judgment and approach
• value simulation results with respect to relevant measures

## Required Knowledge

The course requires one of the following options or equivalent knowledge: 1) 90 ECTS including courses in Mathematical Statistics miminum 12 ECTS and a basic programming course minimum 7,5 ECTS. 2) 90 ECTS including a course in Statistical programming minimum 7,5 ECTS and a basic course in Calculus minimum 7,5 ECTS. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies

## Form of instruction

The teaching mainly consists of lectures.

## Examination modes

Element 1 is examined through a written home exam. Element 2 is examined through written lab reports. For Element 1, one of the following grades is awarded: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). For Element 2, one of the following grades is awarded: Fail (U), or Pass (G). Beyond the judgment Passed, the students can get bonus points for the written exam from the lab reports. The bonus points are only valid on the first two home exams given after the points were awarded. Beyond the judgment Passed, the students can get bonus points for the written exam from the lab reports. The bonus points are only valid on the first two home exams given after the points were awarded. For the whole course, one of the following grades is awarded: Fail (U), Pass (3), Pass with merit (4) or Pass with distinction (5). In order to receive a passing grade on the course, all parts must be completed with a passing grade. The course grade is decided by the judgement on Element 1, and is assigned only when all mandatory examination has been completed.
A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Credit transfers
Students are entitled to an assessment of whether previous education or equivalent knowledge and skills acquired in professional experience can be accredited for equivalent studies at Umeå University. Applications for credit transfers must be sent to Student Services/Degree Evaluation Office. More information on credit transfers can be found on Umeå University's student website, www.student.umu.se, and in the Higher Education Ordinance (Chapter 6). Rejected applications for credit transfers can be appealed (Higher Education Ordinance, Chapter 12) to the Higher Education Appeals Board. This applies regardless of whether the rejection relates to all or parts of the credit transfer application.

## Other regulations

In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics. The course can also be included in the subject area of computational science and engineering.

## Literature

### Valid from: 2018 week 3

Ross Sheldon M.
Simulation
Fifth edition. : 310 p. :
ISBN: 978-0-12-415825-2 (hardback)
Mandatory
Search Album, the University Library catalogue