Inference Theory 2, 7.5 Credits

Contents

The aim of the course is that the student should understand the general principles that constitutes the basic foundation of statistical theory and hence be qualified for contued studies on the PhD level. In the course, basic notions in statistical theory are treated, such as sufficient statistics and the principles of likelihood theory. Different methods for estimation and hypothesis testing, and methods for evaluating them, are also covered.

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding

• prove different properties of maximum likelihood estimates
• derive likelihood ratio tests and the uniformly strongest tests for different situations using limited information

Skills

• derive sufficient statsistics
• apply different method for point and interval estimation
• construct Bayesian estimates
• apply different concepts of convergence

Judgement and approach

• evaluate and compare different estimators and tests from a scientific and ethical perspective.

Required Knowledge

The course requires 90 ECTS including courses in Mathematical Statistics minimum 12 ECTS or courses in Statistics, minimum 75 ECTS and in both cases a course in Basic Calculus, 7,5 ECTS. Proficiency in English equivalent to Swedish upper secondary course English A/5. 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 is mainly in the form of lectures and lessons.

Examination modes

The course is examined by written exams. During the course, the students have the option to hand in written solutions to exercises, that can give bonus points on the exam. The bonus points are only valid on the ordinary exam and on the first re-exam connected to the course occasion on which the exercises are handed out. For the whole course, one of the following grades is assigned: Fail (U), Pass (G), Pass with distinction (VG). In order to receive a passing grade on the course, all parts must be completed with a passing grade. The course grade constitutes a summary of the results on all examination and is assigned only when all mandatory examination has been completed.

A student who has received a passing grade on a test is not allowed to retake the test in order to receive a higher grade. A student who has not received a passing grade after participating in two tests has the right to be assigned another examiner, unless there are certain circumstances prohibiting this (see the Higher Education Ordinance, chapter 6, 22§). A request to be assigned another examiner should be addressed to the head of department for the department of mathematics and mathematical statistics. The possibility of being examined based on the current version of the syllabus is guaranteed for at least two years following the student's first participation in 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.