Statistics

The course enables students to understand and use multilevel models mainly in the context of social science, but examples are also given from medicine and some aspects of biological science. The focus is on multilevel models for quantitative, binary, and multinomial outcomes, with further sessions on models for ordinal and count outcomes. The importance of multilevel modelling for longitudinal data is explained. Analysis is conducted using the Noteable service and the R Stan statistical modelling package, which is free to all users.

This course examines components, decompositions, smoothing and filtering, modelling and forecasting. 

The course presents an application-focused and hands-on approach to learning neural networks and reinforcement learning. It is an introduction to deep learning methods, presenting a wide range of connectionist models that represent the current state-of-the-art. Topics include the fundamentals of machine learning and the mathematical and computational prerequisites for deep learning; feed-forward neural networks, convolutional neural networks, and the recurrent connections to a feed-forward neural network; a brief history of artificial intelligence and neural networks, and reviews open research problems in deep learning and connectionism.  Entry requirements include 90 credits in statistics and a course in linear algebra.

This course provides a fundamental overview of mathematical finance. It begins with an overview of financial contracts, interest rates, and the value of money. Specifically, it discusses what constitutes a fair price for a contract and explains why fair prices are rarely used in everyday transactions. After that, students investigate financial markets in a discrete-time setting, with the help of some revision on basic probability theory. The concept of risk-neutral asset pricing is discussed with reference to pricing stocks and options in the exchange. The last part of the course introduces the fundamental concepts of stochastic calculus and concentrates on continuous time finance with the widely used Black-Scholes model. The goal of this course is to provide students with a broad understanding of the application to finance theory, while setting a solid theoretical foundation to the field. 

The course has a practical focus and introduces students to a range of basic and more advanced network analysis methods through hands-on computer work. Through lectures and readings, students learn key concepts and measures of social network research. In labs, students apply this knowledge through exercises with real-world network datasets using the statistical environment R. The course first covers exploratory Social Network Analysis (SNA) before progressing into more advanced statistical methods.

This course introduces students to the theory, methods, and applications of linear models. The theory of the general linear model is introduced, with an emphasis on widely used methods such as regression analysis, analysis of variance, etc. Applications in various fields are used to give students experience of applying the methods using a specialized statistical software package to analyze linear models.

The course provides an introduction to statistical analysis of text. Methods based on classic statistical approaches (including Bayesian models) and modern approaches such as deep learning (recurrent neural networks) are studied. Topics covered include preprocessing of textual data; text representation; text classification; text clustering; topic modeling; sentiment analysis; and text summarization.

This course helps students develop rigorous quantitative skills to measure market risks in modern financial institutions. It builds on student’s introductory understanding of probability and statistics and focuses on risk management applications. This course illustrates methodologies using real financial data and a number of computer-based workshops.

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.