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Syllabus:

# Design of Experiments and Advanced Statistical Modelling, 15 Credits

Swedish name: Försöksplanering och avancerad statistisk modellering

This syllabus is valid: 2018-12-31 valid to 2025-01-12 (newer version of the syllabus exists)

Course code: 5MS071

Credit points: 15

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
Computational Science and Engineering: Second cycle, has only first-cycle course/s as entry requirements

Established by: Faculty Board of Science and Technology, 2019-02-19

## Contents

The course gives a broad introduction to advanced statistical modelling tools. With the basic theory of linear regression analysis as starting point, the modelling of nonlinear (but parametric) relations between explanatory and response variables, are studied. Furthermore, generalized linear models (GLM) are introduced. In those models, a function of the expected value is modeled, rather than the expected value itself. With GLM, binary response variables (0/1), as well as response variables consisting of counts or proportions, can be handled. The course also covers generalized additive models (GAM), where the dependence between the response variable and the explanatory variables can not be described by any explicit parametric model. The GAM methodology is incorporated into GLM, which enables the modeling of many different types of response variables with complex structures for the dependence of the explanatory variables.

In many industrial applications, one is interested in how a response variable is affected by changes in a number of factors. By systematically changing the factor levels, it is possible to find the optimum of the response variable, in a cost effective way. In the design of experiment part of the course, The theory of the most common tools for systematic planning of experiments and methods for the analysis of experimental results, is covered. Special emphasis is put on complete and fractional two level factorial designs. Response surface methods and their designs, and strategies for sequential design of experiments are included. Finally robust designs are introduced.

As support for choosing experimental designs and analyzing data, throughout the course suitable statistical software is used.

Module 1 (6 ECTS): Advanced Statistical Modelling.
In this Modul linear and nonlinear regression analysis are addressed, including least square error and likelihood methods for estimating the parameters in the models. General Linear Models are introduced and methods for fitting, validating and testing in such models are discussed. Further, the fundamentals of one dimensional smoothing including splines and their use in construction of General Additive Models, are introduced. Some criteria for choosing such model parameters as well as practical aspects of analysis are discussed.

Module 2 (4 ECTS) Design of Experiments.
The theory of the most common tools for systematic planning of experiments and methods for the analysis of experimental results, is covered. ANOVA models are introduced as special cases of general linear models. Special emphasis is put on complete and fractional two level factorial designs. Response surface methods and their designs, and strategies for sequential design of experiments are included. Furthermore, more advanced models for the analysis of variance, with random and mixed effects are treated. Finally robust designs are introduced.

Module 3 (5 ECTS) Computer labs.
The Module covers implementation of the introduced statistical methods with suitable statistical software.

## Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding

• thoroughly describe the concepts simple, multiple and generalized linear models
• thoroughly describe the models that are used for different experimental designs

Skills and abilities

• determine maximum likelihood and least square estimators in one sample and linear regression frameworks
• apply the concepts simple, multiple and generalized linear models, and validate the results of such analyses
• apply the introduced concepts of smoothing of univariate datasets and use them to construct, analyze and validate generalized additive models
• identify and analyze random and mixed effect models
• independently plan and conduct smaller experiments with given resources
• analyse experimental data with suitable software, and draw relevant conclusions
• optimize a response variable with response surface methodology
• analyse dat with robust construction methodology
• present the planning, implementation and analysis of a conducted experiment, in oral and written form

Judgment and approach

• critically validate fitted linear models with respect to relevant measures

## Required Knowledge

The course requires 90 hp including courses in Mathematical Statistics, minimum 15 ECTS or courses in Statistics, minimum 75 ECTS and in both cases a course in basic Computer Programming. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies.

## Form of instruction

The teaching in Modul 1 and 2 takes the form of lectures and lessons. The teaching in Modul 3 takes the form of supervised lab work.

## Examination modes

Modul 1 and 2 is examined by a written home examinations. Modul 3 is examined by written and oral presentations of lab reports. On the written exams, one of the following judgements is assigned: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). On Element 3, one of the following judgements is assigned: Fail (U) or Pass (G). For the whole course, one of the following grades is assigned: Pass (3), Pass with merit (4), Pass with distinction (5). The course grade is decided from the the weighted average of the results on the home examinations, and is assigned only when all mandatory examination has been completed.

Deviations from the form of examination specified in the syllabus form can be made for a student who has been granted pedagogical support due to disability. Individual adaptation of the examination form will be considered based on the student's needs. The examination form is adapted within the framework of the expected learning outcomes of the course syllabus. At the request of the student, the course coordinator, in consultation with the examiner, must promptly decide on the adapted examination form. The decision must then be communicated to the student.

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.