Course syllabus

This course aims to provide students with theoretical and practical knowledge in mathematical and statistical modeling of phenomena such as ocean waves, electricity demand, sensor and radar signals, or option prices in the stock market. The course provides a foundation for further studies in, among other areas, cybernetics, biorobotics, artificial intelligence (AI), machine learning, signal processing, financial mathematics, and time series analysis.

The course includes the following parts:

• Understanding, analyzing, and developing mathematical and statistical models that form the fundamental components of modern machine learning methods.
• Theoretical foundations of robust methods for: parameter estimation and model validation; prediction and interpolation; and modeling time-discrete dynamic stochastic systems, primarily linear.
• Introduction to nonlinear dynamic systems.
• Time series analysis.
• Spectral analysis for time series modeling: identifying underlying patterns and supporting prediction in the frequency-time domain.
• Modeling of time-varying stochastic phenomena.
• Selection of model structure – informed by physical processes or based on observed data.
• Analysis of model properties and predictive performance.
• Estimation of model parameters.
• Considerations of model complexity, computational performance, and measurement error.
• Statistical models and methods for time series analysis.
• Overview of robust methods and outlier detection techniques.
• ARMA processes; least squares (LS) and maximum likelihood (ML) estimation methods, including recursive and adaptive variants.
• Gaussian and non-Gaussian-based modeling approaches.

On completion of the course, the student will be able to:

• Master fundamental statistical methods and their applications in technical subjects, engineering, computer science, and economics.
• Master the statistical principles behind statistical methods for estimation and validation, as well as for prediction and interpolation of linear systems.
• Be familiar with the most important English terminology in the field as a foundation for further studies in, for example, financial statistics and nonlinear time series.
• Understand the impact of large measurement errors and other outlying data, and how these can be detected and handled using statistical models.

On completion of the course, the student will be able to:

• Have knowledge of how to practically collect data, including approaches for applying that knowledge.
• Discuss applications of statistical models and relate them to scientific research problems.
• Design, implement, and test various statistical methods in a given context.
• Evaluate statistical methods, for example, in the context of a machine learning method.

On completion of the course, the student will be able to:

• Draw conclusions from statistical data.
• Propose suitable statistical methods and approaches for problem-solving.
• Critically evaluate others’ choice of methods and the conclusions drawn from them.
• Plan and carry out experiments to evaluate and compare methods, for example, in machine learning.
• Select a statistical method and analyze its performance for a given problem.