This is a graduate course (15 ECTS) in statistical inference. It is aimed at PhD students in Mathematical Statistics, but others are very welcome too. The course covers the foundations of classical and Bayesian statistics and both theories are presented in parallell. Each meeting will be of the type discussion/lecture and there will be reading assignments for each meeting (except the first).
Content and learning outcomes
The purpose of this course is to cover important topics in the theory of statistics in a thorough and general fashion. The course spans over classical inferential techniques including tests of hypothesis, point estimates, and confidence intervals as well as the Bayesian paradigm where one treats all unknown quantities as random variables and constructs a joint probability distribution for all of them. Fundamental concepts are presented from the classical and Bayesian viewpoints in parallel, for better comparison and understanding. Students will practice by studying applications and solving problems related to the theory.
Intended learning outcomes
After completing the course students are expected to
explain the classical and Bayesian paradigms and contrast the two
have a good understanding of sufficient statistics and related concepts
outline the foundations of statistical decision theory, both classical and Bayesian
explain the notion of point estimation, the Cramér-Rao lower bound and the Rao-Blackwell theorem
explain the main results and applications of hypothesis testing
have thorough knowledge of computational methods in statistics, such as the EM-algorithm, the Bootstrap, and Markov Chain Monte Carlo
be able to solve problems and discuss research related questions, related to the theory
The course will consist of two-week cycles with one theory lecture (45 min) the first week and one homework presentation meeting (90 min) the second week.
Literature and preparations
A minimal requirement is a basic course in statistics such as SF1901 and an advanced level course in probability (SF2940), but a graduate course in probability (SF3940) and teaching experience in statistics is recommended.
- Statistical Inference 2nd Ed., G. Casella and R. Berger, Duxbury, 2002.
- Theory of Statistics, M. Schervish, Springer, 1995.
- Information Theory, Inference, and Learning Algorithms, D. Mackay, Cambridge University Press, 2003.
Examination and completion
If the course is discontinued, students may request to be examined during the following two academic years.
- HEM1 - Home assignments, 7.5 credits, grading scale: P, F
- TENM - Oral exam, 7.5 credits, grading scale: P, F
Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.
The examiner may apply another examination format when re-examining individual students.
The examination will be done as a combination of homework and oral exam.
Other requirements for final grade
Homework and oral exam.
Opportunity to complete the requirements via supplementary examination
Opportunity to raise an approved grade via renewed examination
- All members of a group are responsible for the group's work.
- In any assessment, every student shall honestly disclose any help received and sources used.
- In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.
Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.Course web FSF3961