Here, we offer lectures that traditionally do not belong to the core of AI teaching courses, although they are highly relevant to AI. On the one hand, this is Bayesian statistics, which is fundamental for all data-driven methods and from which basic ML concepts can be derived. On the other hand, methods of nonlinear dynamics are increasingly used in new forms of ML.
Bayesian statistics offers a unified approach to data analysis problems. The aim of the lecture is to give an initial introduction to the subject using examples from various fields of science and problems from everyday life. Building on the theoretical foundations, issues such as parameter estimation and hypothesis tests as well as their numerical implementation are dealt with.
Nonlinear effects and collective phenomena that arise from the interaction of many parts can be observed in very different fields of science such as physics, chemistry, biology, medicine, engineering, social sciences or psychology. This includes abrupt transitions between states with completely different properties, multistability or the self-organized creation of spatial, temporal and spatiotemporal order or structures. The lecture is intended to introduce the modeling of such phenomena using examples from various fields of science and to explore the underlying common principles.