Mathematical Statistics

15 credits

Syllabus, Master's level, 1MS013

This course has been discontinued.

A revised version of the syllabus is available.

Code: 1MS013
Education cycle: Second cycle
Main field(s) of study and in-depth level: Mathematics A1N
Grading system: Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by: The Faculty Board of Science and Technology, 15 March 2007
Responsible department: Department of Mathematics

Entry requirements

BSc, Inference Theory

Learning outcomes

In order to pass the course (grade 3) the student should be able to

give an account of important concepts and definitions in the area of the course;

exemplify and interpret important concepts in specific cases;

use the theory, methods and techniques of the course to solve mathematical statistical problems;

express problems from relevant areas of applications in a form suitable for further mathematical statistical analysis, choose suitable models and solution techniques;

interpret and asses results obtained;

present mathematical statistical arguments to others.

Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to treat and solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results.

Requirements concerning the student's ability to present arguments and reasoning are greater.

Content

Probability theory: multidimensional stochastic variables and distributions, conditioning, ordering variables, concepts of convergence in probability theory, multidimensional normal distribution, transforms and their use, central limit theorems and their applications.

Inference theory: statistical models; principles of inference based on likelihood, Fisher information and sufficiency; estimation and estimation methodology, Cramér–Rao's inequality, optimality; test of hypothesis, Neyman Pearson test, uniformly most powerful tests; linear models, the Gauss– Markov theorem, least squares methods.

Instruction

Lectures and problem solving sessions.

Assessment

Separate written examinations in Probability Theory (7 credit points) and Inference Theory (7 credit points) at the end of the course, and an oral examination in Probability Theory (1 credit point). Assignments given during the course may be credited as parts of the final written tests.