Statistical Theory, advanced course, 6 credits

Statistisk teori, fortsättningskurs, 6 hp

TAMS17

Main field of study

Mathematics Applied Mathematics

Course level

Second cycle

Course type

Programme course

Examiner

Torkel Erhardsson

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 0 h
Recommended self-study hours: 160 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 1 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 1 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 1 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 1 Swedish/English Linköping E
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 7 (Autumn 2017) 2 1 Swedish/English Linköping E
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 7 (Autumn 2017) 2 1 Swedish/English Linköping E
6KMAT Mathematics 5 (Autumn 2017) 2 1 Swedish/English Linköping E
6MMAT Mathematics, Master's programme 3 (Autumn 2017) 2 1 Swedish/English Linköping E
6MMAT Mathematics, Master's programme (Mathematics) 3 (Autumn 2017) 2 1 Swedish/English Linköping E

Main field of study

Mathematics, Applied Mathematics

Course level

Second cycle

Advancement level

A1X

Course offered for

  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Mathematics
  • Mathematics, Master's programme
  • Applied Physics and Electrical Engineering - International, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Basic courses in probability theory and statistics. An advanced course in probability theory is helpful, but not required.

Intended learning outcomes

The course gives an introduction to the general theory of statistical inference. After a completed course the student is expected to be able to:

  • describe advanced concepts and theorems of theoretical statistics, e.g., sufficiency, completeness, and the Neyman-Pearson lemma, and to prove some of the theorems.
  • construct suitable, in some cases optimal, point estimators, hypothesis tests, and confidence sets, in general situations where the data are observations from a parametric family of probability distributions.
  • carry out Bayesian inference in general situations where the data are observations from a parametric family of probability distributions.
  • derive asymptotic results for point estimators, hypothesis tests, and confidence sets.
  • understand and assess statistical inference occurring in other undergraduate courses, research reports, or the media.

 

Course content

Exponential families. Location and scale
families. Sufficient, mimimal sufficient, ancillary, and complete
statistics. Methods for point estimation, e.g. maximum likelihood.
Evaluation of point estimates using e.g. the Cramer-Rao inequality and
the Rao-Blackwell theorem. Likelihood ratio tests. Uniformly most
powerful tests and the Neyman-Pearson lemma. The correspondence
between tests and confidence sets. Pivotal variables. Optimality for confidence sets.
Bayesian inference and decision theory. Asymptotic theory.

Teaching and working methods

Lectures and tutorials.

Examination

TEN2Written examination6 creditsU, 3, 4, 5

Grades

Four-grade scale, LiU, U, 3, 4, 5

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Torkel Erhardsson

Course website and other links

http://courses.mai.liu.se/GU/TAMS17

Education components

Preliminary scheduled hours: 0 h
Recommended self-study hours: 160 h

Course literature

Additional literature

Books

  • Casella, G., Berger, R.L, Statistical Inference Duxbury Press
Code Name Scope Grading scale
TEN2 Written examination 6 credits U, 3, 4, 5

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

Additional literature

Books

Casella, G., Berger, R.L, Statistical Inference Duxbury Press

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
1.1 Knowledge of underlying mathematics and science (G1X level)
X
X
X
TEN2

                            
1.2 Fundamental engineering knowledge (G1X level)

                            
1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)

                            
1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)

                            
1.5 Insight into current research and development work

                            
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
2.1 Analytical reasoning and problem solving
X
X
X
TEN2

                            
2.2 Experimentation, investigation, and knowledge discovery
X
X
X
TEN2

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X
TEN2

                            
2.5 Ethics, equity, and other responsibilities
X
TEN2

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork

                            
3.2 Communications
X

                            
3.3 Communication in foreign languages

                            
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
4.1 External, societal, and environmental context

                            
4.2 Enterprise and business context

                            
4.3 Conceiving, system engineering and management

                            
4.4 Designing

                            
4.5 Implementing

                            
4.6 Operating

                            
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development

                            
5.2 Economic conditions for knowledge development

                            
5.3 Identification of needs, structuring and planning of research or development projects

                            
5.4 Execution of research or development projects

                            
5.5 Presentation and evaluation of research or development projects

                            

This tab contains public material from the course room in Lisam. The information published here is not legally binding, such material can be found under the other tabs on this page.

There are no files available for this course.