Theory of linear models (STÆ310M)

Simple and multiple linear regression, analysis of variance and covariance, inference, variances and covariances of estimators, influence and diagnostic analyses using residual and influence measures, simultaneous inference. General linear models as projections with ANOVA as special case, simultaneous inference of estimable functions. R is used in assignments. Solutions to assignments are returned in LaTeX and PDF format.

In addition selected topics will be visited, e.g. generalized linear models (GLMs), nonlinear regression and/or random/mixed effects models and/or bootstrap methods etc.

Students will present solutions to individually assigned
projects/exercises, each of which is handed in earlier through a web-page.

This course is taught in semesters of even-numbered years.

Applied Linear Statistical Models (STÆ312M)

The course focuses on simple and multiple linear regression as well as analysis of variance (ANOVA), analysis of covariance (ANCOVA) and binomial regression. The course is a natural continuation of a typical introductory course in statistics taught in various departments of the university.

We will discuss methods for estimating parameters in linear models, how to construct confidence intervals and test hypotheses for the parameters, which assumptions need to hold for applying the models and what to do when they are not met.

Students will work on projects using the statistical software R.

Theoretical Statistics (STÆ313M)

Likelihood, Sufficient Statistic, Sufficiency Principle, Nuisance Parameter, Conditioning Principle, Invariance Principle, Likelihood Theory. Hypothesis Testing, Simple and Composite Hypothesis, The Neyman-Pearson Lemma, Power, UMP-Test, Invariant Tests. Permutation Tests, Rank Tests. Interval Estimation, Confidence Interval, Confidence, Confidence Region. Point Estimation, Bias, Mean Square Error. Assignments are returned using LaTeX and consitute 20% of the final grade.

Final project (STÆ442L)

Bayesian Data Analysis (STÆ529M)

Goal: To train students in applying methods of Bayesian statistics for analysis of data. Topics: Theory of Bayesian inference, prior distributions, data distributions and posterior distributions. Bayesian inference  for parameters of univariate and multivariate distributions: binomial; normal; Poisson; exponential; multivariate normal; multinomial. Model checking and model comparison: Bayesian p-values; deviance information criterion (DIC). Bayesian computation: Markov chain Monte Carlo (MCMC) methods; the Gibbs sampler; the Metropolis-Hastings algorithm; convergence diagnostistics. Linear models: normal linear models; hierarchical linear models; generalized linear models. Emphasis on data analysis using software, e.g. Matlab and R.

Stochastic Processes (STÆ415M)

Introduction to stochastic processes with main emphasis on Markov chains.

Subject matter: Hitting time, classification of states, irreducibility, period, recurrence (positive and null), transience, regeneration, coupling, stationarity, time-reversibility, coupling from the past, branching processes, queues, martingales, Brownian motion.

Time Series Analysis (IÐN113F)

ARMAX and other similar time series models. Non-stationary time series. Correlation and spectral analysis. Parameter estimation, parametric and non-parametric approaches, Least Squares and Maximum Likelihood. Model validation methods. Models with time dependent parameters. Numerical methods for minimization. Outlier detection and interpolation. Introduction to nonlinear time series models. Discrete state space models. Discrete state space models. Extensive use of MATLAB, especially the System Identification Toolbox.

Thesis skills: project management, writing skills and presentation (VON001F)

Introduction to the scientific method. Ethics of science and within the university community.
The role of the student, advisors and external examiner. Effective and honest communications.
Conducting a literature review, using bibliographic databases and reference handling. Thesis structure, formulating research questions, writing and argumentation. How scientific writing differs from general purpose writing. Writing a MS study plan and proposal. Practical skills for presenting tables and figures, layout, fonts and colors. Presentation skills. Project management for a thesis, how to divide a large project into smaller tasks, setting a work plan and following a timeline. Life after graduate school and being employable.

Statistical Consulting (MAS201M)

Participants in the course will obtain training in practical statistics as used when providing general statistical counselling. The participants will be introduced to actual statistical projects by assisting students in various departments within the university. The participants will report on the projects in class, discuss options for solving the projects and subsequently assist the students with analyses using R and interpretation of results.

Final project (STÆ442L)

Applied data analysis (MAS202M)

The course focuses on statistical analysis using the R environment. It is assumed that students have basic knowledge of statistics and the statistical software R. Students will learn to apply a broad range of statistical methods in R (such as classification methods, resampling methods, linear model selection and tree-based methods). The course on 12 weeks and will be on "flipped" form. This means that no lectures will be given but students will read some material and watch videos before attending classes. Students will then work on assignments during the classes.

Random Effects Models (STÆ004F)

The focus of this course is on Bayesian latent Gaussian models (BLGMs) which are a class of Bayesian hierarchical models and applications of these models. The main topics are three types of BLGMs: (i) Bayesian Gaussian—Gaussian models, (ii) BLGMs with a univariate link function, and (iii) BLGMs with a multivariate link function, as well as prior densities for BLGMs and posterior computation for BLGMs. In the first part of the course, the basics of these models is covered and homework assignments will be given on these topics. In the second part of the course, the focus is on a project, in which data are analyzed using BLGMs. Each student can contribute data that she or he wishes to analyze. The material in the course is based on a theoretical background. However, the focus on data analysis is strong, and computation and programming play a large role in the course. Thus, the course will be useful to students in their future projects involving data analysis.

Linear regression models, the multiple normal distribution, hierarchical models, fixed and random effect models, restricted maximum likelihood estimation, best linear unbiased estimators, Bayesian inference, statistical decision theory, Markov chains,  Monte Carlo integration, importance sampling, Markov chain Monte Carlo, Gibbs sampling, the Metropolis-Hastings algorithm.

Literature Study for the Master's Degree in Statistics (STÆ017F)

The supervising committee and the MS-student meet for one semester on a weekly basis to discuss research articles, review articles, and parts of books selected by the committee for that purpose. The reading material shall be related to the student's field of research, but without overlapping with the research project, so as to broaden the horizons of the student. The course is completed with a short thesis on the subject and an oral examination.

Introduction to Measure-Theoretic Probability (STÆ418M)

Probability based on measure-theory.

Subject matter: Probability, extension theorems, independence, expectation. The Borel-Cantelli theorem and the Kolmogorov 0-1 law. Inequalities and the weak and strong laws of large numbers. Convergence pointwise, in probability, with probability one, in distribtution, and in total variation. Coupling methods. The central limit theorem. Conditional probability and expectation.