Statistics

This course provides an introduction to programming within the statistical package R. Various computer-intensive statistical algorithms are discussed and their implementation in R is investigated. Topics to include basic commands of R (including plotting graphics); data structures and data manipulation; writing functions and scripts; optimizing functions in R; and programming statistical techniques and interpreting the results (including bootstrap algorithms).

The course covers sufficient statistics, factorization criteria, exponential families, Rao-Blackwells theorem, ancillary statistics, Cramér-Rao's bound, Neyman-Pearson's lemma, permutation test, and connection between hypothesis testing and confidence intervals. Asymptotic methods: maximum likelihood estimation, profile, conditional and penalized likelihood as well as hypothesis testing with likelihood ratio-, Wald- and score-method. Bayesian inference: estimation, hypothesis testing, and confidence interval and the difference compared to frequentist interpretation.

Have you heard of Big Data or AI? What about Data Science? Data Science is the field of study that deals with data acquisition, data analysis, and decision making with domain knowledge. In the discipline of Data Science, data refer to either structured or unstructured data, which is commonly referred to as Big Data. Tools for analyzing Big Data in Data Science are called machine learning that is a sub-field of Statistics, and machine learning is known as a workhorse of AI. This mathematical statistics course is designed to provide a comprehensive introduction to the mathematical study of statistics (or machine learning). Without the knowledge of mathematical statistics, you cannot fully understand machine learning algorithms including Deep Learning. Topics include probability, random variables, univariate or multivariate distributions, elementary statistical inference, and limiting distributions. Emphasis is on the theoretical development and practical implementation of each topic, including definitions, theorems, proofs, computer programming, and simulations.

Prerequisites: STA1001. Introduction to Statistics (or equivalent course), STA1002. Calculus (or equivalent course)

Topics in this statistics for psychology course include: basic concepts of measurement and types of variables; data summarization and visualization; measures of central tendency, variability, and skewness; measures of association; probability theory; probability distributions of some continuous and discrete random variables; sampling.

What is a reasonable value for a derivative on the financial market? The course consists of two related parts. The first part looks at option theory in discrete time. The purpose is to introduce fundamental concepts of financial markets such as free of arbitrage and completeness as well as martingales and martingale measures. Tree structures to model time dynamics of stock prices and information flows are used. The second part studies models formulated in continuous time. The models used are formulated as stochastic differential equations (SDE:s). The theories behind Brownian motion, stochastic integrals, Ito-'s formula, measures changes, and numeraires are presented and applied to option theory both for the stock and the interest rate markets. Students derive e.g. the Black-Scholes formula and how to create a replicating portfolio for a derivative contract.

This course examines the foundation for statistics and data science skills that are needed for a career in science and for further study in applied statistics and data science. It covers exploring data, modelling data, sampling data and making decisions with data. Students will use problems and data from the physical, health, life and social sciences to develop adaptive problem-solving skills in a team setting. 

In the course, students practice descriptive evaluations as well as inferential statistical analyses with R: In addition to the most common univariate methods, non-parametric and selected multivariate methods are also taken into account. Further focuses are on the diverse options for creating diagrams and data management. After completing the course, participants can carry out standard exploratory and inferential statistical procedures with R, create flexible diagrams and have gained an overview of the diverse possible uses of the additional packages for special problems.

This course focuses on data analysis, an algorithmic-driven method of extracting text from (large) corpora, in literary and historical sources and social media.  The course includes a mini big data project to provide hands-on experience and an understanding of the affordances and limitations of data analysis methods. No background in the methods or programming skills is needed. Easy-to-learn web-based tools and software are used. Theoretically, the course explores how the representation of text in more visual formats which are typically removed from its semantic contexts, offers opportunities for both new insights as well as misrepresentation. Concepts covered include distant reading, algorithmic visualization, and data feminism. This course helps students become more savvy users of digital information: the implications and challenges that methods and technologies pose to conventional research, analysis, and publication in the arts, humanities, and social sciences, including issues such as transparency, authenticity, and bias.

Environmental management professionals frequently require the ability to understand and work with quantitative data. This course unit starts by introducing the practical and ethical implications of working with quantitative data. Following this, content provides grounding in different data sources, exploring varied data types and the processes required before any visualization or analysis can occur. The course then explores different analytical methods that can be used to facilitate interpretation and presentation of outputs related to environmental management professions, including inferential statistics and the foundations of basic computer coding.