Advanced Statistical Modelling, 7.5 Credits

Contents

Element 1 (5 hp): Theory. In this Element 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.

Element 2 (2.5 hp) Computer labs. The Element 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

Skills

• 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
• given data, identify suitable regression model for it based on the proper prior analysis
• apply the statistical methods introduced during the course using a suitable statistical software and analyze the output.
• present the results of the analyses in written form

Judgement and approach

• critically validate fitted linear models with respect to relevant measures

Required Knowledge

The course requires a total of 90 ECTS including courses in Mathematical Statistics minimum 12 ECTS and a course in basic Computer Programming or equivalent knowledge. Proficiency in English equivalent to Swedish upper secondary course English 5/A. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.

Form of instruction

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

Examination modes

Element 1 is assessed through a written examination. Element 2 is assessed 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). For the course as whole, one of the following grades is awarded: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). The grade for the whole course is determined by the grade given for Element 1. To pass the whole course, all elements must have been passed. The grade is only set once all compulsory elements have been assessed.

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 transfer
All students have the right to have their previous education or equivalent, and  their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university, http://www.student.umu.se, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications

Other regulations

This course can not be included in a degree together with another course with similar contents. When in doubt, the student should consult the director of study at the department of mathematics and mathematical statistics. The course can also be included in the subject area of computational science and engineering.