NMAK20004U Statistics B
MSc Programme in Statistics
The course covers a number of modern statistical models and methods, mathematical methods for analyzing them, and mathematical relations between the different methods.
The course will cover the following content
- Elements of statistical decision theory
- Asymptotic and finite sample error bounds
- Non-parametric hypotheses about functional relations, e.g. hypotheses about smoothness or shape constraints
- High-dimensional regression including Poisson and logistic regression
- Sparse discrete and Gaussian graphical models
The mathematical content will be presented together with a mix of practical applications demonstrating how the models and methods are used for data analysis.
- Loss functions and risk minimization
- Standard inequalities from probability theory
- Non-parametric model assumptions e.g. via series expansions
- Error bounds under common, non-parametric assumptions, e.g. smoothness, shape constraint or sparsity
- Penalized regression, including ridge regression and lasso
- Graphical lasso
- Perform theoretical analyses of statistical methods under parametric or non-parametric model assumptions.
- Discuss the limitations of the models and methods covered
- Derive error bounds based on the theory covered
- Ability to interpret theoretical results in the context of practical data analysis, including how complex models with many covariates can be analyzed and the results interpreted
- Analysis of complex regression models with a large number of covariates
- Translation between joint models and regression models
- Translation of a scientific hypothesis into either a parametric or a non-parametric mathematical hypothesis
See Absalon for a list of course literature.
It is recommended that the course Regression is taken no later than at the same time as this course.
Academic qualifications equivalent to a BSc degree is recommended.
- 7,5 ECTS
- Type of assessment
- Written examination, 4 hours under invigilation...
- Exam registration requirements
There will be 3 group assignments (up to two students). The students have to hand-in these assignments, which then need to get approved.
- Written aids allowed
- Marking scale
- 7-point grading scale
- Censorship form
- No external censorship
One internal examiner
25 minutes oral exam without preparation time. No aids allowed. If the mandatory assignments have not been approved during the course the non-approved assignment(s) must be handed in no later than three weeks before the beginning of the re-exam week. The assignments must be approved before the re-exam.
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.