Stochastic Foundations
This course offers a mathematical introduction to probability theory and statistics, covering foundational concepts such as probability spaces, random variables, distributions, and expectations.
Overview
The course provides a mathematical introduction to fundamental concepts and methods in probability theory and statistics. Initially, it offers a formal understanding of probability theory by covering probability spaces, random variables, distributions, expected values, and central convergence results. Subsequently, it introduces methods from descriptive and inferential statistics, which are used for data description, estimation of key figures, and hypothesis testing.
Which topics will be covered?
- Formal definition of stochastic models
- Central results of probability theory
- Methods from descriptive statistics for data visualization and characterization
- Methods from inferential statistics for parameter estimation and hypothesis testing
What will I achieve?
On completion of the course you will be able to…
- understand and categorize standard machine learning methods
- analyze and interprete data using statistical methods
Which prerequisites do I need to fulfill?
• Basic knowledge in linear algebra and algebra
• Basic knowledge in function theory
• Basic knowledge in differential and integral calculus
