Statistics

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.

This course examines the practical knowledge and skills of some advanced analytics and statistical modeling problems.

The course is devoted to understanding the fundamentals of descriptive and inferential statistics (concepts, rationale of analyses, and their assumptions), and to the application of techniques on data sets. It starts with a definition of basic concepts relevant to all statistical tests, eg chance and odds, randomness, data levels, and probability distributions. Systematic errors and random errors are discussed concerning their impact on the reliability and validity of data. Concepts explained include the sampling distribution, standard error, test statistics, chosen (alpha) and observed (p-value) significance level, type I and type II error, the power of a test, confidence intervals, and effect size measures. Research designs that are widely used in applied science research and relate these to different types of samples are used. The lab sessions include data sets to be checked and summarized using appropriate descriptive statistical techniques. Data transformations are applied where needed.

This course is part of the Laurea Magistrale degree program and is intended for advanced level students. Enrolment is by permission of the instructor. The course is graded P/NP only. The course covers the main skills related to data communication: design of a data communication product, from the sourcing and interpretation of data to their graphic representation; and the creation of data visualizations, charts, and dashboards using the main tools of the industry. For both of these points, there are practical exercises, to gain mastery in specific data visualization tools or to favor a creative design process. The course discusses key topics related to these two skills, such as: evaluating accessibility and inclusivity of data communication products; the elements of visual and info design; audience-driven design; perception and bias, and their influence in data communication; exercises of creativity in the representation of data; a focus on maps and geo data; and a critical evaluation of data visualizations, to improve the efficiency and clarity communication products.

This course establishes the foundation of a wide range of statistical learning methods. It aims to understand and utilize the fundamentals of various statistical learning models. 

The course covers:

• statistical learning;
• classical linear methods for regression and classification; 
• cross-validation;
• bootstrap; 
• modern linear methods;
• nonlinear methods; 
• tree-based methods;
• support vector machines;
• unsupervised learning;
• neural networks, and
• deep learning. 

These topics are the basics of statistical learning, but the core of machine learning. By the end of this course, students will have easier access to and understanding of deep learning and artificial intelligence.

The course requires the following prerequisites: 

• Python Basic – this course assumes a basic knowledge of Python
• STAT 241: Matrix Theory or Linear Algebra - provides a computational foundation for understanding statistical models.
• STAT 232: Mathematical Statistics- knowledge of probability theory and asymptotic evaluations.