Statistics

This course provides research training for exchange students. Students work on a research project under the guidance of assigned faculty members. Through a full-time commitment, students improve their research skills by participating in the different phases of research, including development of research plans, proposals, data analysis, and presentation of research results. A pass/no pass grade is assigned based a progress report, self-evaluation, midterm report, presentation, and final report.

The course provides a basic understanding of the probabilistic models and techniques underlying the most widely used classes of stochastic processes. The main focus is on modeling aspects, which are completed by a description of some popular algorithms for simulation. Mathematical concepts are integrated with real-world applications and examples and illustrated through simulations. At the end of the course, students will have bridged the gap between their elementary probability skills and the knowledge required to understand and use basic models based on stochastic processes. The course discusses topics including conditional probabilities and conditional expectations; introduction to stochastic processes and Markov chains; discrete-time Markov chains: Chapman-Kolmogorov equation, Classification of states, Limiting properties, and Applications (e.g. stochastic models, sequential testing, and website ranking); introduction to Stochastic Simulation, Simulation techniques, and Monte Carlo methods; Markov Chain Monte Carlo algorithms, and Computational applications; counting processes and the Poisson process, Continuous-time stochastic processes, and examples and modeling applications. The course requires students to have solid knowledge of calculus and basic probability theory (e.g. probability distributions and random variables) as a prerequisite. Some knowledge of basic programming tools (such as R) is also required.

The course covers key statistical methods and data analytic techniques most relevant to finance. Hands-on experience in analyzing financial data in the “R” environment is an essential part of the course. The course includes a selection of the following topics: obtaining financial data, low- and high-frequency financial time series, ARCH-type models for low-frequency volatilities and their simple alternatives, Markowitz portfolio theory and the Capital Asset Pricing Model, concepts and  practices in machine learning as applied in financial forecasting, Value at Risk. The course covers classification techniques using random forests and simple trading strategies if time permits.

This course introduces basic concepts and methods of statistics as a tool to perform appropriate data analyses. The statistical software R is taught alongside the material to introduce statistical computing. Students learn to load raw data, make numerical and graphical summaries of data, and conduct various estimation and testing procedures. Topics include programming in R, descriptive statistics, concepts of probability, random variables and probability distributions, sampling distribution, statistical estimation, hypothesis testing, linear regression, and applications to real-world problems.

This course covers basic concepts of information theory, and discusses how these concepts are used in machine learning and data science. The first part of the course introduces various information-theoretic quantities including Entropy, Mutual Information, KL-divergence, and provides two main components of information theory: source coding and channel coding. The second part covers how information theory is used in machine learning and data science. Topics include various applications including recommendation systems, supervised learning, generative models, neural network compression, and distributed machine learning. 

The course introduces students to basic principles of artificial intelligence (AI) systems. By AI, we refer to machines (or computers) that mimic cognitive functions that humans associate with the human mind, such as learning and problem solving. The course takes a practical approach, explaining the main principles and methods used in the design of AI systems. The course provides an introduction to main principles of deep learning, covering topics of neural nets as universal approximators, design of neural network architectures, backpropagation and optimization methods for training neural networks, and some special deep neural network architectures commonly used for solving AI tasks such as image classification, sequence modelling, natural language processing and generative models. If time allows, this course also provides an introduction to reinforcement learning problem formulation. Students gain practical knowledge to learn and evaluate deep learning and reinforcement learning algorithms (if time allows) using Python and open-source software libraries.

This course emphasizes hands-on laboratory experience and teaches students research background, relevant theories, and basic laboratory techniques relevant to their field of study. Students formulate a research plan, implement it by conducting experiment-based research, and convey the results in scholarly presentations. Students submit a written research report at the end of the course.

This course prepares students to use simple quantitative methods in their dissertations, and provides the conceptual tools needed to produce, commission, evaluate, and interpret statistical information in professional contexts. It provides a brief but systematic introduction to three forms of data collection: sample surveys, experiments, and content analysis. It explains the theory behind these techniques, the form that they would ideally take, the compromises that are made in order to conduct them in the real world, and the consequences which those compromises have for the reliability of findings. Students create proposals for quantitative research projects, analyze pre-prepared datasets, and receive an introduction to the practicalities of data collection by jointly designing and conducting a piece of survey research. 

This course provides an introduction to the theory and practice of using social media data for research and enables the development of transferable research and data skills. Such skills are in demand in the research and consultancy profession across the public and private sectors. After reviewing the different data types including Facebook and Twitter, students consider how to access and analyze such data. This, in part, includes developing the student’s critical data skills, hands-on training, and practice analyses on real social media data such as coding Tweets and blogs. This involves the use of on-line software to gather social media data. The course involves the development of research design skills including hypothesis testing, data analysis, and interpretation and writing skills. The emphasis on the use of real data to answer questions is designed to engage students and for them to consider using such approaches as part of their own dissertation research.

This course covers basic concepts of database management systems, including relational and other types of database management systems. The topics covered include basic concepts of the relational model, creating and modifying relations using Structured Query Language (SQL), basic SQL queries using SELECT operator, nested queries, aggregate operators such as GROUP BY, integrity constraints and relations, views, application development using JDBC, Internet protocols such as HTTP and XML, storage and indexing, tree-structured indexing using B+ trees, hash-based indexing, query evaluation and algorithms for relational operations, external sorting, transaction management and concurrency, database schema and normal forms, and overview of NoSQL databases such as key-value stores, document, and graph databases. The course demonstrates how various theoretical principles are implemented in practice in a database management system, such as MySQL, SQLite and PostgreSQL.